Maths-
General
Easy
Question
Explain how to identify an extraneous solution for an equation containing a radical expression
Hint:
Write the reason.
The correct answer is: extraneous.
Complete step by step solution:
First find the solution, then substitute the solutions in the original equation and if the
answer results in an illogical equation then the answer is extraneous.
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Maths-
Solve the equation ![square root of x plus 2 end root plus square root of 3 x plus 4 end root equals 2](data:image/png;base64,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)
Solve the equation ![square root of x plus 2 end root plus square root of 3 x plus 4 end root equals 2](data:image/png;base64,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)
Maths-General
Maths-
Solve the equation ![square root of 2 x minus 5 end root minus square root of x minus 3 end root equals 1](data:image/png;base64,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)
Solve the equation ![square root of 2 x minus 5 end root minus square root of x minus 3 end root equals 1](data:image/png;base64,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)
Maths-General
Maths-
Solve the equation ![left parenthesis 3 x plus 2 right parenthesis to the power of 2 over 5 end exponent equals 4](data:image/png;base64,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)
Solve the equation ![left parenthesis 3 x plus 2 right parenthesis to the power of 2 over 5 end exponent equals 4](data:image/png;base64,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)
Maths-General
Maths-
Simplify each expressions and state the domain : ![fraction numerator x cubed plus 4 x squared minus x minus 4 over denominator x squared plus 3 x minus 4 end fraction](data:image/png;base64,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)
Simplify each expressions and state the domain : ![fraction numerator x cubed plus 4 x squared minus x minus 4 over denominator x squared plus 3 x minus 4 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Express the rational expression in its lowest terms .
![fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction](data:image/png;base64,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)
A rational expression is a fractional form containing polynomials on the denominator and the numerator.
Express the rational expression in its lowest terms .
![fraction numerator x squared minus 2 x minus 3 over denominator 2 x squared minus 3 x minus 5 end fraction](data:image/png;base64,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)
Maths-General
A rational expression is a fractional form containing polynomials on the denominator and the numerator.
Maths-
When Multiplying
, is it necessary to make the restriction x ≠ 0 ? Why or Why not ?
When Multiplying
, is it necessary to make the restriction x ≠ 0 ? Why or Why not ?
Maths-General
Maths-
Identify the slope and y-intercept of the line: ![y equals 1 fourth x plus 5](data:image/png;base64,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)
Identify the slope and y-intercept of the line: ![y equals 1 fourth x plus 5](data:image/png;base64,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)
Maths-General
Maths-
Rewrite the equation
to isolate x.
Rewrite the equation
to isolate x.
Maths-General
Maths-
Find the product of the rational expression
![fraction numerator 8 x minus 3 plus 3 x squared over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 4 over denominator x plus 3 end fraction](data:image/png;base64,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)
Find the product of the rational expression
![fraction numerator 8 x minus 3 plus 3 x squared over denominator 2 x squared minus x minus 6 end fraction cross times fraction numerator x squared minus 4 over denominator x plus 3 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Explain how you can tell whether a rational expression is in simplest form?
Explain how you can tell whether a rational expression is in simplest form?
Maths-General
Maths-
Determine whether is sometimes
, always or never true . Justify your reasoning.
Determine whether is sometimes
, always or never true . Justify your reasoning.
Maths-General
Maths-
Identify the slope and y-intercept of the line: ![y equals negative 5 x minus 3 over 4](data:image/png;base64,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)
Identify the slope and y-intercept of the line: ![y equals negative 5 x minus 3 over 4](data:image/png;base64,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)
Maths-General
Maths-
Find the extraneous solution of ![square root of 8 x plus 9 end root equals x](data:image/png;base64,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)
Find the extraneous solution of ![square root of 8 x plus 9 end root equals x](data:image/png;base64,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)
Maths-General
Maths-
Explain the similarities between rational numbers and rational expressions ?
Explain the similarities between rational numbers and rational expressions ?
Maths-General
Maths-
Simplify the following expression.
![open parentheses fraction numerator 2 x minus 1 over denominator x plus 3 end fraction minus fraction numerator x squared minus 4 over denominator 2 x plus 1 end fraction close parentheses space cross times space fraction numerator 2 x squared plus 7 x plus 3 over denominator x plus 2 end fraction](data:image/png;base64,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)
Simplify the following expression.
![open parentheses fraction numerator 2 x minus 1 over denominator x plus 3 end fraction minus fraction numerator x squared minus 4 over denominator 2 x plus 1 end fraction close parentheses space cross times space fraction numerator 2 x squared plus 7 x plus 3 over denominator x plus 2 end fraction](data:image/png;base64,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)
Maths-General