a)
\(\dfrac{x^3+2x^2-x-2}{x^3-3x+2}\)
\(=\dfrac{x^2\left(x+2\right)-\left(x+2\right)}{x^3-4x+x+2}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{x\left(x^2-4\right)+\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{x\left(x-2\right)\left(x+2\right)+\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{\left(x+2\right)\left(x^2-2x+1\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{\left(x+2\right)\left(x-1\right)^2}\)
\(=\dfrac{x+1}{x-1}\)
b):
\(\dfrac{3x^2-7xy+4y^2}{2x^2+2xy-4y^2}\)
\(=\dfrac{3x^2-3xy-4xy+4y^2}{2x^2-2xy+4xy-4y^{ 2}}\)
\(=\dfrac{3x\left(x-y\right)-4y\left(x-y\right)}{2x\left(x-y\right)+4y\left(x-y\right)}\)
\(=\dfrac{\left(x-y\right)\left(3x-4y\right)}{\left(x-y\right) \left(2x+4y\right)}\)
\(=\dfrac{3x-4y}{2x+4y}\)
c):
\(\dfrac{x^2+5x}{2x+10}\)
\(=\dfrac{x\left(x+5\right)}{2\left(x+5\right)}\)
\(=\dfrac{x}{2}\)
\(\dfrac{x^3+2x^2-x-2}{x^3-3x+2}\)
= \(\dfrac{\left(x^3+2x^2\right)-\left(x+2\right)}{x^3-x-2x+2}\)
=\(\dfrac{x^2\left(x+2\right)-\left(x+2\right)}{\left(x^3-x\right)-\left(2x-2\right)}\)
= \(\dfrac{\left(x^2-1\right)\left(x+2\right)}{x\left(x^2-1\right)-2\left(x-1\right)}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left[x\left(x+1\right)-2\right]}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2+x-2\right)}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2-x+2x-2\right)}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left[\left(x^2-x\right)+\left(2x-2\right)\right]}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left[x\left(x-1\right)+2\left(x-1\right)\right]}\)
= \(\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x-1\right)\left(x+2\right)}\)
= \(\dfrac{x+1}{x-1}\)
Mk thấy câu b) cứ sai sai kiểu j ý
c) \(\dfrac{x^2+5x}{2x+10}\)
= \(\dfrac{x\left(x+5\right)}{2\left(x+5\right)}\)
= \(\dfrac{x}{2}\)
d):
\(\dfrac{2x^2-9x+7}{-2x^2-x+28}\)
\(=\dfrac{2x^2-2x-7x+7}{-2x^2-8x+7x+28}\)
\(=\dfrac{2x\left(x-1\right)-7\left(x-1\right)}{-2x\left(x+4\right)+7\left(x+4\right)}\)
\(=\dfrac{\left(x-1\right)\left(2x-7\right)}{\left(x+4\right)\left(-2x+7\right)}\)
\(=\dfrac{\left(x-1\right)\left(2x-7\right)}{\left(-x-4\right)\left(2x-7\right)}\)
\(=-\dfrac{x-1}{x+4}\)
e):
\(\dfrac{x^3+3x^2-2}{x^3+3x+4}\)
\(=\dfrac{x^3+x^2+2x^2-2}{x^3-x+4x+4}\)
\(=\dfrac{x^2\left(x+1\right)+2\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)\left(x+1\right)+4\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x^2+2x-2\right)}{\left(x+1\right)\left(x^2-x+4\right)}\)
\(=\dfrac{x^2+2x-2}{x^2-x+4}\)
