Bài 3:
a: ĐKXĐ: \(x\notin\left\{0;5\right\}\)
\(\dfrac{x^2-10x+25}{x^2-5x}\)
\(=\dfrac{\left(x-5\right)^2}{x\left(x-5\right)}\)
\(=\dfrac{x-5}{x}\)
b: ĐKXĐ: \(x\notin\left\{1;-1\right\}\)
\(\dfrac{x}{2\left(x-1\right)}+\dfrac{x-2}{x^2-1}-\dfrac{5}{2x+2}\)
\(=\dfrac{x}{2\left(x-1\right)}+\dfrac{x-2}{\left(x-1\right)\left(x+1\right)}-\dfrac{5}{2\left(x+1\right)}\)
\(=\dfrac{x\left(x+1\right)+2\left(x-2\right)-5\left(x-1\right)}{2\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2+x+2x-4-5x+5}{2\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2-2x+1}{2\left(x+1\right)\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{2\left(x+1\right)\left(x-1\right)}=\dfrac{x-1}{2\left(x+1\right)}\)
Bài 2:
a: \(4x^2-4y^2\)
\(=4\left(x^2-y^2\right)\)
\(=4\left(x-y\right)\left(x+y\right)\)
b: \(x^2-4y^2-2x+4y\)
\(=\left(x^2-4y^2\right)-\left(2x-4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+2y-2\right)\)
c: \(x^2-xy+2x-2y\)
\(=\left(x^2-xy\right)+\left(2x-2y\right)\)
\(=x\left(x-y\right)+2\left(x-y\right)\)
=(x-y)(x+2)
d: \(6x^2-7x+2\)
\(=6x^2-3x-4x+2\)
\(=3x\left(2x-1\right)-2\left(2x-1\right)\)
=(2x-1)(3x-2)
Bài 1:
a: \(x\left(x-5\right)+\left(x+3\right)\left(3-x\right)\)
\(=x^2-5x+9-x^2\)
=-5x+9
b: \(\left(8x^3y^4-12x^4y^3\right):4x^2y^2-2xy^2\)
\(=\dfrac{8x^3y^4-12x^4y^3}{4x^2y^2}-2xy^2\)
\(=2xy^2-3x^2y-2xy^2\)
\(=-3x^2y\)
