Maths-
General
Easy

Question

What is the Quotient of  fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction straight & fraction numerator x squared plus 3 x minus 4 over denominator 2 x plus 6 end fraction.

hintHint:

The expansion of the identity, left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b.
We are asked to find the quotient of the given expression.

The correct answer is: the quotient of the expression is 2(x + 2)/(x + 4)


    Step 1 of 2:
    The given expression is: fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction divided by fraction numerator x squared plus 3 x minus 4 over denominator 2 x plus 6 end fraction.
    Take the reciprocal of the second expression and multiply it with the first expression. It serves the same effect as division;
    fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 x plus 6 over denominator x squared plus 3 x minus 4 end fraction
    Step 2 of 2:
    Simplify the expression and cancel out the common factors;
    fraction numerator x squared plus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 x plus 6 over denominator x squared plus 3 x minus 4 end fraction equals fraction numerator x squared plus 2 x minus x minus 2 over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator x squared plus 4 x minus x minus 4 end fraction
    equals fraction numerator x left parenthesis x plus 2 right parenthesis minus 1 left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator x left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis end fraction
    equals fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis over denominator x plus 3 end fraction cross times fraction numerator 2 left parenthesis x plus 3 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis end fraction
    equals fraction numerator 2 left parenthesis x plus 2 right parenthesis over denominator x plus 4 end fraction
    Thus, the quotient of the expression is: fraction numerator 2 left parenthesis x plus 2 right parenthesis over denominator x plus 4 end fraction.

    Division of two expressions is the same as taking the reciprocal of the second expression and multiplying it with the first expression.

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