Maths-
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Easy

Question

What is the simplified form of fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x squared plus x over denominator 5 x minus 10 end fraction

hintHint:

The expansions of some identities are:
left parenthesis x plus a right parenthesis squared equals x squared plus 2 a x plus a squared
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 simplify the expression.

The correct answer is: The simplified expression is: .


    Step 1 of 2:
    Simplify the numerators of the expression using identities.
    fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator x squared plus x minus 6 over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x squared plus x over denominator 5 x minus 10 end fraction equals fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator x squared plus 3 x minus 2 x minus 6 over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x left parenthesis x plus 1 right parenthesis over denominator 5 x minus 10 end fraction
    equals fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator x left parenthesis x plus 3 right parenthesis minus 2 left parenthesis x plus 3 right parenthesis over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x left parenthesis x plus 1 right parenthesis over denominator 5 x minus 10 end fraction
    equals fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x left parenthesis x plus 1 right parenthesis over denominator 5 x minus 10 end fraction
    We simplified the second expression 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.
    Step 2 of 2:
    Simplify the denominator of the expression and cut of the common terms.
    fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis over denominator x squared plus 2 x plus 1 end fraction cross times fraction numerator x left parenthesis x plus 1 right parenthesis over denominator 5 x minus 10 end fraction equals fraction numerator 5 x over denominator x plus 3 end fraction cross times fraction numerator left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared end fraction cross times fraction numerator x left parenthesis x plus 1 right parenthesis over denominator 5 left parenthesis x minus 2 right parenthesis end fraction
    equals fraction numerator x squared over denominator left parenthesis x plus 1 right parenthesis end fraction
    The identity used here is: left parenthesis x plus a right parenthesis squared equals x squared plus 2 a x plus a squared
    The simplified expression is: fraction numerator x squared over denominator left parenthesis x plus 1 right parenthesis end fraction

    You could simplify an expression by removing common values form the numerator and the denominator.

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