Question

Riley makes a mistake in step 2 while doing her homework. what was her mistake? startfraction x over x squared minus 5 x 6 endfraction startfraction x over x 3 endfraction

Answer 1

She used wrong common denominator.

Correct solution:

$\frac{x}{{x}^2-5x+6} + \frac{3}{x+3}\\\\=\frac{x}{{x}^2 - 3x - 2x + 6} + \frac{3}{x+3}\\\\=\frac{x}{(x-3)(x-2)} + \frac{3}{x+3}\\\\=\frac{x(x+3) + 3(x-2)(x-3)}{(x-3)(x-2)(x+3)}\\\\=\frac{{x}^2 + 3x + 3{x}^2-15x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{4{x}^2 -12x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{2(2{x}^2 - 6x + 9)}{(x-3)(x-2)(x+3)}$

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