Maths-
General
Easy

Question

If the denominator of a rational expression is x cubed plus 3 x squared minus 10 x  what values must be restricted from the domain for x ?

hintHint:

The expansion of  left parenthesis straight x plus straight a right parenthesis left parenthesis straight x plus straight b right parenthesis text  is  end text straight x squared plus left parenthesis straight a plus straight b right parenthesis straight x plus ab. We have to state the domain of a rational expression while simplifying them because we must exclude zeros of a denominator as dividing with zero is not defined.
We are asked to find the values that have to be restricted for the domain of a expression containing the given expression as the denominator.

The correct answer is: Thus, the values to be excluded from the domain are 0, 2 straight & minus 5


    Step 1 of 2:
    Given denominator of an expression isx left parenthesis x minus 2 right parenthesis left parenthesis x plus 5 right parenthesis equals 0.
    Simplifying it, we have:
    straight x cubed plus 3 straight x squared minus 10 straight x equals straight x open parentheses straight x squared plus 3 straight x minus 10 close parentheses
    equals straight x open parentheses straight x squared plus 5 straight x minus 2 straight x minus 10 close parentheses

    equals straight x left parenthesis straight x left parenthesis straight x plus 5 right parenthesis minus 2 left parenthesis straight x plus 5 right parenthesis right parenthesis
    equals straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x plus 5 right parenthesis
    Step 2 of 2:
    Here, the denominator attains a zero value when straight x left parenthesis straight x minus 2 right parenthesis left parenthesis straight x plus 5 right parenthesis equals 0. That is;
    straight x equals 0 comma straight x equals 2 straight & straight x equals negative 5.
    Thus, the values to be excluded from the domain are 0, 2 straight & minus 5.

    We have to state the domain of a rational expression while simplifying them because we must exclude zeros of a denominator as dividing with zero is not defined.

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