Carcass wrote:

For \(x \neq 2\) and \(x \neq 3\) , \(\frac{-2}{x-2} + \frac{x}{x-3}=\)

A. \(1\)

B. \(\frac{1}{x-3}\)

C. \(\frac{x-2}{2x-5}\)

D. \(\frac{-2x}{(x-2)(x-3)}\)

E. \(\frac{x^2-4x+6}{(x-2)(x-3)}\)

GIVEN: \(\frac{-2}{x-2} + \frac{x}{x-3}=\)

Rewrite with common denominators: \(\frac{(-2)(x-3)}{(x-2)(x-3)} + \frac{(x)(x-2)}{(x-3)(x-2)}\)

Simplify numerators: \(\frac{-2x+6}{(x-2)(x-3)} + \frac{x^2-2x}{(x-3)(x-2)}\)

Combine fractions: \(\frac{(-2x+6)+(x^2-2x)}{(x-2)(x-3)}\)

Simplify numerator: \(\frac{x^2-4x+6}{(x-2)(x-3)}\)

Answer: E

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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