1: \(\left(5x-4\right)^2-\left(5x-1\right)\left(5x-16\right)\)
\(=25x^2-40x+16-\left(25x^2-80x-5x+16\right)\)
\(=25x^2-40x+16-\left(25x^2-85x+16\right)\)
\(=25x^2-40x+16-25x^2+85x-16\)
=85x-40x
=45x
2: \(\left(3x^3-10x^2-7x+20\right):\left(3x-4\right)\)
\(=\left(3x^3-4x^2-6x^2+8x-15x+20\right):\left(3x-4\right)\)
\(=\frac{x^2\cdot\left(3x-4\right)-2x\left(3x-4\right)-5\left(3x-4\right)}{3x-4}=x^2-2x-5\)
3: \(\left(8x^3-y^3\right):\left(4x^2+2xy+y^2\right)\)
\(=\frac{\left(2x-y\right)\left(4x^2+2xy+y^2\right)}{4x^2+2xy+y^2}\)
=2x-y
4: \(\frac{x^2}{x-5}+\frac{5x}{5-x}\)
\(=\frac{x^2-5x}{x-5}\)
\(=\frac{x\left(x-5\right)}{x-5}=x\)
5: \(A=\frac{x^2-3xy-x+3y}{x^2-3xy}\)
\(=\frac{x\left(x-3y\right)-\left(x-3y\right)}{x\left(x-3y\right)}=\frac{\left(x-3y\right)\left(x-1\right)}{x\left(x-3y\right)}=\frac{x-1}{x}\)
Khi x=-3 thì \(A=\frac{-3-1}{-3}=\frac{-4}{-3}=\frac43\)
7: \(\frac{2}{x+2}+\frac{2}{x-2}-\frac{7x-6}{x^2-4}\)
\(=\frac{2}{x+2}+\frac{2}{x-2}-\frac{7x-6}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{2x-4+2x+4-7x+6}{\left(x-2\right)\left(x+2\right)}=\frac{-3x+6}{\left(x-2\right)\left(x+2\right)}=\frac{-3}{x+2}\)
