Question

rút gọn
a) 2x - 2y / x^2 - 2xy + y^2
b) 2 -2a / a^3 - 1
c) x^2 - 6x + 9 / x^2 - 8x + 15
d) x^4 - 2x^3 / 2x^4 - x^3

Answer 1

a) \(\dfrac{2x-2y}{x^2-2xy+y^2}=\dfrac{2\left(x-y\right)}{\left(x-y\right)^2}=\dfrac{2}{x-y}\)

b) \(\dfrac{2-2a}{a^3-1}=-\dfrac{2-2a}{1-a^3}=-\dfrac{2\left(1-a\right)}{\left(1-a\right)\left(1+a+a^2\right)}=\dfrac{-2}{\left(1+a+a^2\right)}\)

Answer 2

c) \(\dfrac{x^2-6x+9}{x^2-8x+15}\)

\(=\dfrac{x^2-2.x.3+3^2}{x^2-3x-5x+15}\)

\(=\dfrac{\left(x-3\right)^2}{\left(x^2-3x\right)-\left(5x-15\right)}\)

\(=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)-5\left(x-3\right)}\)

\(=\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x-5\right)}\)

\(=\dfrac{x-3}{x-5}\)

d) \(\dfrac{x^4-2x^3}{2x^4-x^3}\)

\(=\dfrac{x^3\left(x-2\right)}{x^3\left(2x-1\right)}\)

\(=\dfrac{x-2}{2x-1}\)