Question

Solve for x
$\frac{4x-3}{2x+1}-10\left(\frac{2x+1}{4x-3}\right)=3,x\ne \frac{-1}{2},\frac{3}{4}$

Answer 1

$\frac{4x-3}{2x+1}-10\left(\frac{2x+1}{4x-3}\right)=3\frac{4x-3}{2x+1}=kk-10\frac{1}{k}=3k^2-10=3k{k}^2-3k-10=0k^2-5k+2k-10=0k(k-5)+2(k-5)=0(k+2)(k-5)=0k=5,-2\frac{4x-3}{2x+1}=5;\frac{4x-3}{2x+1}=-24x-3=10x+5;4x-3=-4x-26x+8=0;8x-1=0x=-\frac{8}{6};x=-\frac{1}{8}x=\frac{-4}{3},\frac{-1}{8}$