Question

Х-2/х+3-30/х^2-9=1/6

Answer 1

$\frac{x-2}{x+3}-\frac{30}{x^2-9}=\frac16\\O.D.3.:\\\begin{cases}x+3\neq0\\x^2-9\neq0\end{cases}\Rightarrow\begin{cases}x+3\neq0\\(x-3)(x+3)\neq0\end{cases}\Rightarrow\begin{cases}x\neq-3\\x\neq3\end{cases}\\\\\frac{x-2}{x+3}-\frac{30}{(x+3)(x-3)}=\frac16\\\frac{(x-2)(x-3)-30}{x^2-9}=\frac16\\\frac{x^2-5x-24}{x^2-9}\\6x^2-30x-144=x^2-9\\5x^2-30x-135=0\;\;\;\div5\\x^2-6x-27=0\\D=36+4\cdot27=144=(12)^2\\x_{1,2}=\frac{6\pm12}2\\x_1=-3\;-\;He\;nogx.\;no\;O.D.3.\\x_2=9\\OTBET:\;9$