Question

Find all solutions to the problem: 2/x+6 - 1/x+3 =2​

Answer 1

Answer:

$\displaystyle x=-\frac{9}{2},\:x=-4$

Step-by-step explanation:

$\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36$

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4$