Question

What two rational expressions sum to 2x+3x2−2x−15?

Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

Answer 1

The rational expressions that sum to  $\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}$

The given expression is:

$\frac{2x+3}{x^2-2x-15}$

Factorize the denominator

$x^2-2x-15\\x^2-5x+3x-15\\x(x-5)+3(x-5)\\(x+3)(x-5)$

The given expression therefore becomes:

$\frac{2x+3}{(x+3)(x-5)}$

This can be split into the sum:

$\frac{2x+3}{(x+3)(x-5)} = \frac{2x}{(x+3)(x-5)} + \frac{3}{(x+3)(x-5)}$

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