## Intermediate Algebra for College Students (7th Edition)

Solution set: $\{2\}$
Factor the denominators $x^{2}-x=x(x-1)$ $x^{2}-1=(x-1)(x+1)$ LCD = $x(x-1)(x+1)$ $\displaystyle \frac{x+2}{x(x-1)}-\frac{6}{(x-1)(x+1)}=0$ Exclude solutions which yield 0 in denominators: $x\not\in\{0,-1,1\}\qquad (*)$ Multiply with the LCD, $x(x-1)(x+1)$ $(x+2)(x+1)-6\cdot x=0$ $x^{2}+3x+2-6x=0$ $x^{2}-3x+2=0$ ... factors of 2 whose sum is -3 ... are -1 and -2 $(x-1)(x-2)=0\qquad$ ... apply the zero product principle $x=1\qquad$ ... is excluded, see (*). $x=2$ Solution set: $\{2\}$