perform the indicated operations and simplify
x-2/x-4 - x+1/x+4 + x-20/x^2-16

Question

jim_thompson5910 · Answer

$$\Large \frac{x-2}{x-4} - \frac{x+1}{x+4}+\frac{x-20}{x^2-16}$$



$$\Large \frac{x-2}{x-4} - \frac{x+1}{x+4}+\frac{x-20}{(x-4)(x+4)}$$



$$\Large \frac{(x-2)(x+4)}{(x-4)(x+4)} - \frac{x+1}{x+4}+\frac{x-20}{(x-4)(x+4)}$$



$$\Large \frac{x^2+2x-8}{(x-4)(x+4)} - \frac{x+1}{x+4}+\frac{x-20}{(x-4)(x+4)}$$



$$\Large \frac{x^2+2x-8}{(x-4)(x+4)} - \frac{(x+1)(x-4)}{(x-4)(x+4)}+\frac{x-20}{(x-4)(x+4)}$$



$$\Large \frac{x^2+2x-8}{(x-4)(x+4)} - \frac{x^2-3x-4}{(x-4)(x+4)}+\frac{x-20}{(x-4)(x+4)}$$



$$\Large \frac{x^2+2x-8-(x^2-3x-4)+x-20}{(x-4)(x+4)}$$



$$\Large \frac{x^2+2x-8-x^2+3x+4+x-20}{(x-4)(x+4)}$$



$$\Large \frac{6x-24}{(x-4)(x+4)}$$



$$\Large \frac{6(x-4)}{(x-4)(x+4)}$$



$$\Large \frac{6\cancel{(x-4)}}{\cancel{(x-4)}(x+4)}$$



$$\Large \frac{6}{x+4}$$



So $$\Large \frac{x-2}{x-4} - \frac{x+1}{x+4}+\frac{x-20}{x^2-16} = \frac{6}{x+4}$$