Maths-
General
Easy

Question

What is the quotient of fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction divided by fraction numerator x squared plus 5 x plus 4 over denominator x squared plus 3 x minus 4 end fraction

hintHint:

To find the quotient is just to divide the expressions. To divide an expression, multiply the first rational expression by the reciprocal of the second rational expression.
We are asked to find the quotient of the expression.

The correct answer is: ( x - 1 )/ x + 1


    Step 1 of 3:
    The given expression is.fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction divided by fraction numerator x squared plus 5 x plus 4 over denominator x squared plus 3 x minus 4 end fraction
    Multiply it by taking the reciprocal of the second expression, fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction cross times fraction numerator x squared plus 3 x minus 4 over denominator x squared plus 5 x plus 4 end fraction
    Step 2 of 3:
    Now, simplify the expression,fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction using the identity,open parentheses x squared minus a squared close parentheses equals left parenthesis x minus a right parenthesis left parenthesis x plus a right parenthesis
    fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction equals fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 plus x right parenthesis end fraction
    Simplify the expression, fraction numerator x squared plus 3 x minus 4 over denominator x squared plus 5 x plus 4 end fraction using 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
    fraction numerator x squared plus 3 x minus 4 over denominator x squared plus 5 x plus 4 end fraction equals fraction numerator x squared plus 4 x minus x minus 4 over denominator x squared plus 4 x plus x plus 4 end fraction
    equals fraction numerator x left parenthesis x plus 4 right parenthesis minus 1 left parenthesis x plus 4 right parenthesis over denominator x left parenthesis x plus 4 right parenthesis plus 1 left parenthesis x plus 4 right parenthesis end fraction
    equals fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x plus 4 right parenthesis over denominator left parenthesis x plus 4 right parenthesis left parenthesis x plus 1 right parenthesis end fraction
    equals fraction numerator left parenthesis x minus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis end fraction
    Step 3 of 3:
    Multiply the simplified expression;
    fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction cross times fraction numerator x squared plus 3 x minus 4 over denominator x squared plus 5 x plus 4 end fraction equals fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 plus x right parenthesis end fraction cross times fraction numerator left parenthesis x minus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis end fraction
    equals fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 plus x right parenthesis end fraction cross times negative fraction numerator left parenthesis 1 minus x right parenthesis over denominator left parenthesis x plus 1 right parenthesis end fraction
    equals negative fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator left parenthesis 1 plus x right parenthesis squared end fraction

    The quotient of an expression is the value you get when you divide them. It can be done by taking the reciprocal of the second expression and then multiplying it.

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