Question

\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)

Answer 1

\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\) dkxd : \(x\ne-1;x\ne-3\)

\(\Leftrightarrow\frac{2x\left(x+1\right)}{2\left(x+3\right)\left(x+1\right)}-\frac{2x\left(x+3\right)}{2\left(x+3\right)\left(x+1\right)}=\frac{2\left(3x+2\right)}{2\left(x+3\right)\left(x+1\right)}\)

\(\Leftrightarrow2x^2+2x-2x^2-6x=6x+4\)

\(\Leftrightarrow-10x=4\)

\(\Leftrightarrow x=\frac{-4}{10}=\frac{-2}{5}\)

Vậy S = \(\left\{-\frac{2}{5}\right\}\)