Maths-
General
Easy
Question
Find the Quotient and the domain .
![fraction numerator straight x to the power of 4 plus straight x cubed minus 30 straight x squared over denominator straight x squared minus 3 straight x minus 18 end fraction divided by fraction numerator straight x cubed plus straight x squared minus 30 straight x over denominator straight x squared minus 36 end fraction](data:image/png;base64,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)
Hint:
The expansions of certain identities are:
![table attributes columnalign right columnspacing 0em end attributes row cell left parenthesis straight x plus straight a right parenthesis left parenthesis straight x plus straight b right parenthesis equals straight x squared plus left parenthesis straight a plus straight b right parenthesis straight x plus ab end cell row cell open parentheses straight x squared minus straight a squared close parentheses equals left parenthesis straight x minus straight a right parenthesis left parenthesis straight x plus straight a right parenthesis space space space space space space space space space space space space space space end cell end table](data:image/png;base64,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)
Finding the quotient is same as division. Dividing a number and multiplying it with a reciprocal of the number have the same effect.
We are asked to find the quotient and the domain of the expression.
The correct answer is: Hence, the domain of the expression is, (-∞,-3)∪(-3,∞)
Step 1 of 3:
The given expression is
.
Take the reciprocal of the second expression and then multiply them;
![fraction numerator straight x to the power of 4 plus straight x cubed minus 30 straight x squared over denominator straight x squared minus 3 straight x minus 18 end fraction cross times fraction numerator straight x squared minus 36 over denominator straight x cubed plus straight x squared minus 30 straight x end fraction](data:image/png;base64,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)
Step 2 of 3:
Simplify the expression and cancel out the common factors;
![table attributes columnalign right columnspacing 0em end attributes row cell fraction numerator straight x to the power of 4 plus straight x cubed minus 30 straight x squared over denominator straight x squared minus 3 straight x minus 18 end fraction cross times fraction numerator straight x squared minus 36 over denominator straight x cubed plus straight x squared minus 30 straight x end fraction equals fraction numerator straight x squared open parentheses straight x squared plus straight x minus 30 close parentheses over denominator straight x squared minus 6 straight x plus 3 straight x minus 18 end fraction cross times fraction numerator open parentheses straight x squared minus 6 squared close parentheses over denominator straight x open parentheses straight x squared plus straight x minus 30 close parentheses end fraction end cell row cell equals fraction numerator straight x left parenthesis straight x minus 6 right parenthesis left parenthesis straight x plus 6 right parenthesis over denominator straight x left parenthesis straight x minus 6 right parenthesis plus 3 left parenthesis straight x minus 6 right parenthesis end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end 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)
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell space space space space space equals fraction numerator x left parenthesis x minus 6 right parenthesis left parenthesis x plus 6 right parenthesis over denominator left parenthesis x plus 3 right parenthesis left parenthesis x minus 6 right parenthesis end fraction end cell row cell equals fraction numerator x left parenthesis x plus 6 right parenthesis over denominator x plus 3 end fraction space space space space space space space space space space end cell end table](data:image/png;base64,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)
Thus, the quotient of the expression is:![fraction numerator x left parenthesis x plus 6 right parenthesis over denominator x plus 3 end fraction](data:image/png;base64,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)
Step 3 of 3:
The domain of a rational expression should exclude the value for which the denominator attains a zero value. Thus, we have:
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x plus 3 equals 0 end cell row cell x equals negative 3 space space space end cell end table](data:image/png;base64,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)
Hence, the domain of the expression is, (-∞,-3)∪(-3,∞)
We have to state the domain of a rational expression while simplifying them because we must exclude zeros of a denominator as dividing with zero is not defined.
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Maths-
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
Find the approximate annual interest rate for a five year auto loan of $40,000 that has monthly payments of $750.
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
Find the approximate annual interest rate for a five year auto loan of $40,000 that has monthly payments of $750.
Maths-General
Maths-
Order from least to greatest ![29 over 12 comma 2.4444 horizontal ellipsis comma square root of 5.65](data:image/png;base64,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)
Order from least to greatest ![29 over 12 comma 2.4444 horizontal ellipsis comma square root of 5.65](data:image/png;base64,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)
Maths-General
Maths-
Find the Quotient and the domain .
![fraction numerator 25 straight x squared minus 4 over denominator straight x squared minus 9 end fraction divided by fraction numerator 5 straight x minus 2 over denominator straight x plus 3 end fraction](data:image/png;base64,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)
Find the Quotient and the domain .
![fraction numerator 25 straight x squared minus 4 over denominator straight x squared minus 9 end fraction divided by fraction numerator 5 straight x minus 2 over denominator straight x plus 3 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Order from least to greatest
0.363636..... , √15 , ![square root of 17 over 3 end root](data:image/png;base64,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)
Order from least to greatest
0.363636..... , √15 , ![square root of 17 over 3 end root](data:image/png;base64,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)
Maths-General
Maths-
Becky is competing in an 8-mi road race. She runs at a constant speed of 6 mi/h. Write an in slope-intercept form to represent the distance Becky has left to run.
Becky is competing in an 8-mi road race. She runs at a constant speed of 6 mi/h. Write an in slope-intercept form to represent the distance Becky has left to run.
Maths-General
Maths-
Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
![13.9 comma space square root of 49 comma space minus 48](data:image/png;base64,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)
Recognize the following numbers as real numbers , rational numbers , irrational numbers , integers ,whole numbers :
![13.9 comma space square root of 49 comma space minus 48](data:image/png;base64,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)
Maths-General
Maths-
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
a. Find the approximate annual interest rate for a four year signature loan $20,000 that has monthly payments of $500.
The Approximate annual interest rate r of a monthly installment loan is given by the formula:
![r equals fraction numerator fraction numerator 24 left parenthesis n m minus p right parenthesis over denominator n end fraction over denominator open parentheses p plus fraction numerator n m over denominator 12 end fraction close parentheses end fraction](data:image/png;base64,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)
Where n is the total number of payments , m is the monthly payment and p is the amount financed.
a. Find the approximate annual interest rate for a four year signature loan $20,000 that has monthly payments of $500.
Maths-General
Maths-
The line
passes through the points
.Find b, n, and p.
The line
passes through the points
.Find b, n, and p.
Maths-General
Maths-
Find the Quotient and the domain .
![fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction divided by fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction](data:image/png;base64,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)
Find the Quotient and the domain .
![fraction numerator left parenthesis straight x minus straight y right parenthesis squared over denominator straight x plus straight y end fraction divided by fraction numerator 3 straight x plus 3 straight y over denominator straight x squared minus straight y squared end fraction](data:image/png;base64,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)
Maths-General
Maths-
For What value of X is
undefined ?
For What value of X is
undefined ?
Maths-General
Maths-
Give an example of two irrational numbers whose product is rational .
Give an example of two irrational numbers whose product is rational .
Maths-General