Maths-
General
Easy

Question

Find the product and the domain ?
fraction numerator straight x plus 5 over denominator straight x cubed minus 25 straight x end fraction cross times 2 straight x cubed minus 11 straight x squared plus 5 straight x

hintHint:

The expansions of certain identities are:
table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis straight x plus straight a right parenthesis squared equals straight x squared plus 2 ax plus straight a squared end cell row cell open parentheses straight x squared minus straight a squared close parentheses equals left parenthesis straight x minus straight a right parenthesis left parenthesis straight x plus straight a right parenthesis end cell end table
We are asked to find the product and the domain of the given expression.

The correct answer is: the answer is bellow


    Step 1 of 2:
    Simplify the expression and hence find the product,
    table attributes columnalign right columnspacing 0em end attributes row cell fraction numerator straight x plus 5 over denominator straight x cubed minus 25 straight x end fraction cross times 2 straight x cubed minus 11 straight x squared plus 5 straight x equals fraction numerator straight x plus 5 over denominator straight x open parentheses straight x squared minus 25 close parentheses end fraction cross times straight x space open parentheses 2 straight x squared minus 11 straight x plus 5 close parentheses end cell row cell equals fraction numerator straight x plus 5 over denominator straight x open parentheses straight x minus 5 squared close parentheses end fraction cross times straight x space open parentheses 2 straight x squared minus 10 straight x minus 1 straight x plus 5 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator x plus 5 over denominator x left parenthesis x minus 5 right parenthesis left parenthesis x plus 5 right parenthesis end fraction cross times x left parenthesis 2 x left parenthesis x minus 5 right parenthesis minus 1 left parenthesis x minus 5 right parenthesis right parenthesis end cell row cell equals fraction numerator x plus 5 over denominator x left parenthesis x minus 5 right parenthesis left parenthesis x plus 5 right parenthesis end fraction cross times x left parenthesis 2 x minus 1 right parenthesis left parenthesis x minus 5 right parenthesis space space space space space space space space end cell row cell equals 2 x minus 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table
    The product of the expression is: 2x - 1.
    Step 2 of 2
    The product of the expression is, 2x - 1 which is a polynomial. Thus, the domain of the product is the set of real numbers.

    The domain of any polynomial is the set of real numbers.

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