\(P=\frac{\left(\frac{2x-3}{4x^2-12x+5}+\frac{2x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right)}{\left(\frac{21+2x-8x^2}{4x^2+4x-3}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{4x^2-2x-10x+5}+\frac{-2\left(4-x\right)}{8x-2x^2+5x-20}-\frac{3}{2x-1}\right)}{\left(\frac{21-12x+14x-8x^2}{4x^2+6x-2x-3}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{2x\left(2x-1\right)-5\left(2x-1\right)}+\frac{-2\left(4-x\right)}{2x\left(4-x\right)-5\left(4-x\right)}-\frac{3}{2x-1}\right)}{\left(\frac{3\left(7-4x\right)+2x\left(7-4x\right)}{2x\left(2x+3\right)-\left(2x+3\right)}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}+\frac{-2\left(4-x\right)}{\left(2x-5\right)\left(4-x\right)}-\frac{3}{2x-1}\right)}{\frac{\left(7-4x\right)\left(3+2x\right)}{\left(2x+3\right)\left(2x-1\right)}}+1\)
\(=\frac{\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}+\frac{-2\left(2x-1\right)}{\left(2x-1\right)\left(2x-5\right)}-\frac{3\left(2x-5\right)}{\left(2x-1\right)\left(2x-5\right)}\right)}{\frac{7-4x}{2x-1}}+1\)
\(=\frac{2x-3-4x+2-6x+15}{\left(2x-1\right)\left(2x-5\right)}\times\frac{2x-1}{7-4x}+1\)
\(=\frac{14-8x}{2x-5}\times\frac{1}{7-4x}+1\)
\(=\frac{2\left(7-4x\right)}{2x-5}\times\frac{1}{7-4x}+\frac{2x-5}{2x-5}\)
\(=\frac{2+2x-5}{2x-5}\)
\(=\frac{2x-3}{2x-5}\)
