Question

\(\frac{2x-3}{2x^2+5x-12}-\frac{2x-3}{2x^2+3x-9}=0\)

Answer 1

\(\frac{2x-3}{2x^2+5x-12}-\frac{2x-3}{2x^2+3x-9}=0\\ \Leftrightarrow\frac{2x-3}{\left(2x-3\right)\cdot\left(x+4\right)}-\frac{2x-3}{\left(2x-3\right)\cdot\left(x+3\right)}=0\\\Leftrightarrow\frac{1}{x+4}-\frac{1}{x+3}=0\\ \Leftrightarrow\frac{x+3}{\left(x+4\right)\cdot\left(x+3\right)}-\frac{x+4}{\left(x+4\right)\cdot\left(x+3\right)}=0\\ \Leftrightarrow\frac{x+3-x-4}{\left(x+4\right)\cdot\left(x+3\right)}=0\\ \Leftrightarrow\frac{-1}{\left(x+4\right)\cdot\left(x+3\right)}=0\\ \Leftrightarrow-1=0\\ \Rightarrow x\in\varnothing\)