Question

Add or subtract the following expressions by finding a common denominator, and then simplifying your answer

Answer 1

Solution

1.

$\frac{6}{x+1}-\frac{5}{x-2}=\frac{6(x-2)-5(x+1)}{(x+1)(x-2)}=\frac{6x-12-5x-5}{(x+1)(x+2)}=\frac{x-17}{(x+1)(x+2)}$

2.

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