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\(P=\frac{\left(\frac{2x-3}{4x^2-12x+5}+\frac{2x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right)}{\left(\frac{21+2x-8x^2}{4x^2+4x-3}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{4x^2-2x-10x+5}+\frac{-2\left(4-x\right)}{8x-2x^2+5x-20}-\frac{3}{2x-1}\right)}{\left(\frac{21-12x+14x-8x^2}{4x^2+6x-2x-3}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{2x\left(2x-1\right)-5\left(2x-1\right)}+\frac{-2\left(4-x\right)}{2x\left(4-x\right)-5\left(4-x\right)}-\frac{3}{2x-1}\right)}{\left(\frac{3\left(7-4x\right)+2x\left(7-4x\right)}{2x\left(2x+3\right)-\left(2x+3\right)}\right)}+1\)
\(=\frac{\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}+\frac{-2\left(4-x\right)}{\left(2x-5\right)\left(4-x\right)}-\frac{3}{2x-1}\right)}{\frac{\left(7-4x\right)\left(3+2x\right)}{\left(2x+3\right)\left(2x-1\right)}}+1\)
\(=\frac{\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}+\frac{-2\left(2x-1\right)}{\left(2x-1\right)\left(2x-5\right)}-\frac{3\left(2x-5\right)}{\left(2x-1\right)\left(2x-5\right)}\right)}{\frac{7-4x}{2x-1}}+1\)
\(=\frac{2x-3-4x+2-6x+15}{\left(2x-1\right)\left(2x-5\right)}\times\frac{2x-1}{7-4x}+1\)
\(=\frac{14-8x}{2x-5}\times\frac{1}{7-4x}+1\)
\(=\frac{2\left(7-4x\right)}{2x-5}\times\frac{1}{7-4x}+\frac{2x-5}{2x-5}\)
\(=\frac{2+2x-5}{2x-5}\)
\(=\frac{2x-3}{2x-5}\)
Bài 2: \(a,\frac{7x-1}{2x^2+6x}=\frac{7x-1}{2x\left(x+3\right)}=\frac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(\frac{5-3x}{x^2-9}=\frac{5-3x}{\left(x-3\right)\left(x+3\right)}=\frac{\left(5-3x\right)2x}{2x\left(x-3\right)\left(x+3\right)}\)
\(b,\frac{x+1}{x-x^2}=\frac{x+1}{x\left(1-x\right)}=-\frac{x+1}{x\left(x+1\right)}=-\frac{2\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)^2}\)
\(\frac{x+2}{2-4x+2x^2}=\frac{x+2}{2\left(x-1\right)^2}=\frac{2x\left(x+2\right)}{2x\left(x-1\right)^2}\)
\(c,\frac{4x^2-3x+5}{x^3-1}=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{2x}{x^2+x+1}=\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{6}{x-1}=\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(d,\frac{7}{5x}=\frac{7.2\left(2y-x\right)\left(2y+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{4}{x-2y}=-\frac{4}{2y-x}=-\frac{4.2.5x\left(2x+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{x-y}{8y^2-2x^2}=\frac{x-y}{2\left(4y^2-x^2\right)}=\frac{x-y}{2\left(2y-x\right)\left(2y+x\right)}=\frac{5x\left(x-y\right)}{2.5x.\left(2y-x\right)\left(2y+x\right)}\)