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Find the difference of the question below I have the question and answer choices listed. Any incorrect answers or links will be removed.Thanks in advance <3

Find the difference of the question below I have the question and answer choices listed-example-1

1 Answer

5 votes

Given :


(5x)/(x^2-x-6)-(4)/(x^2+4x+4)

We need to factor the polynomial in the denominator.


(5x)/(x^2-x-6)-(4)/(x^2+4x+4)=(5x)/(x^2-3x+2x-6)-(4)/(x^2+2*2x+2^2)


=\frac{5x}{x(x^{}-3)+2(x-3)}-(4)/((x+2)^2)


=\frac{5x}{(x^{}-3)(x+2)}-(4)/((x+2)^2)

The least common multiple of (x-3)(x+2) and (x+2)(x+2) is (x-3)(x+2)(x+2), so making the denominatore (x-3)(x+2)(x+2).


=\frac{5x(x+2)}{(x^{}-3)(x+2)^2}-(4(x-3))/((x-3)(x+2)^2)


=\frac{5x^2+10x}{(x^{}-3)(x+2)^2}-(4x-12)/((x-3)(x+2)^2)


=\frac{5x^2+10x-4x+12}{(x^{}-3)(x+2)^2}


=\frac{5x^2+6x+12}{(x^{}-3)(x+2)^2}

Hence the difference of the given is


\frac{5x^2+6x+12}{(x^{}-3)(x+2)^2}

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