Question

Simplify the following two polynomials in the simplest form: $\frac{x-2}{x^2-7x+10}+\frac{x+3}{x^2-2x-15}$

• A. $\frac{2}{x-5}$
• B. $\frac{2}{x+5}$
• C. $\frac{4}{x-5}$
• D. None of these

Answer 1

The correct option is A $\frac{2}{x-5}$

The given expression $\frac{x-2}{x^2-7x+10}+\frac{x+3}{x^2-2x-15}$can be simplified as shown below:

$=\frac{x-2}{x^2-7x+10}+\frac{x+3}{x^2-2x-15}$

$=\frac{x-2}{x^2-5x-2x+10}+\frac{x+3}{x^2-5x+3x-15}$

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

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

$=\frac{1}{x-5}+\frac{1}{x-5}$

$=\frac{1+1}{x-5}$

$=\frac{2}{x-5}$

Hence, $\frac{x-2}{x^2-7x+10}+\frac{x+3}{x^2-2x-15}=\frac{2}{x-5}$.