Maths-
General
Easy

Question

Find the simplified form of each product , and give the domain.
fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction cross times open parentheses 2 x cubed minus 3 x squared minus 5 x close parentheses

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 find simplified form of each product and their domain.

The correct answer is: Now find the values for which the denominator takes zero value. 3x + 1 = 0 3x = - 1


    ANSWER:fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction
    Step 1 of 3:
    Simplify the expression, fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction
    fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction equals fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction
    equals fraction numerator x open parentheses x squared minus 4 close parentheses over denominator 6 x squared minus 15 x plus 2 x minus 5 end fraction
    equals fraction numerator x open parentheses x squared minus 2 squared close parentheses over denominator 3 x left parenthesis 2 x minus 5 right parenthesis plus 1 left parenthesis 2 x minus 5 right parenthesis end fraction
    equals fraction numerator x left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator left parenthesis 3 x plus 1 right parenthesis left parenthesis 2 x minus 5 right parenthesis end fraction
    Now, simplify the expression,
    open parentheses 2 x cubed minus 3 x squared minus 5 x close parentheses equals x open parentheses 2 x squared minus 3 x minus 5 close parentheses
    equals x open parentheses 2 x squared minus 5 x plus 2 x minus 5 close parentheses
    equals x left parenthesis x left parenthesis 2 x minus 5 right parenthesis plus 1 left parenthesis 2 x minus 5 right parenthesis right parenthesis
    equals x left parenthesis x plus 1 right parenthesis left parenthesis 2 x minus 5 right parenthesis
    Step 2 of 3:
    Find the product of the simplified expression:
    fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction cross times open parentheses 2 x cubed minus 3 x squared minus 5 x close parentheses equals fraction numerator x left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator left parenthesis 3 x plus 1 right parenthesis left parenthesis 2 x minus 5 right parenthesis end fraction cross times space x left parenthesis x plus 1 right parenthesis left parenthesis 2 x minus 5 right parenthesis
    equals fraction numerator x squared left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis left parenthesis x plus 1 right parenthesis over denominator left parenthesis 3 x plus 1 right parenthesis end fraction
    Step 3 of 3:
    Now find the values for which the denominator takes zero value.
    3 x plus 1 equals 0
    3 x equals negative 1
    x equals fraction numerator negative 1 over denominator 3 end fraction
    Thus, the domain of the expression is open parentheses negative straight infinity comma negative 1 third close parentheses union open parentheses negative 1 third comma straight infinity close parentheses

    When you find the domain of a rational expression exclude the values that bring zero to the denominator.

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