Question

x/(2x-3) + x/(2x+2) = 2x/(x+1) (x-3)

Answer 1

\(\frac{x}{2x-3}+\frac{x}{2x+2}=\frac{2x}{\left(x+1\right)\cdot\left(x-3\right)}\\ \Leftrightarrow\frac{x}{2x-3}+\frac{x}{2\cdot\left(x+1\right)}=\frac{2x}{\left(x+1\right)\cdot\left(x-3\right)}\\ \Leftrightarrow2x\cdot\left(x+1\right)\cdot\left(x-3\right)+x\cdot\left(2x-3\right)\cdot\left(x-3\right)=4x\cdot\left(2x-3\right)\\ \Leftrightarrow4x^3-13x^2+3x=8x^2-12x\\ \Leftrightarrow4x^3-13x^2+3x-8x^2+12x=0\\ \Leftrightarrow4x^3-21x^2+15x=0\\ \Leftrightarrow x\cdot\left(4x^2-21x+15\right)=0\\ \Rightarrow x=0\)