Question

4. Quy đồng mẫu thức các phân thức:

a) \(\dfrac{1}{x+2},\dfrac{8}{2x-x^2}\)

b) \(x^2+1,\dfrac{x^4}{x^2-1}\)

c) \(\dfrac{x^3}{x^3-3x^2y+3xy^2-y^3},\dfrac{x}{y^2-xy}\)

Answer 1

a: \(\dfrac{1}{x+2}=\dfrac{2x-x^2}{x\left(2-x\right)\left(2+x\right)}\)

\(\dfrac{8}{2x-x^2}=\dfrac{8}{x\left(2-x\right)}=\dfrac{8x+16}{x\left(2-x\right)\left(2+x\right)}\)

b: \(x^2+1=\dfrac{x^4-1}{x^2-1}\)

\(\dfrac{x^4}{x^2-1}=\dfrac{x^4}{x^2-1}\)

c: \(\dfrac{x^3}{x^3-3x^2y+3xy^2-y^3}=\dfrac{x^3}{\left(x-y\right)^3}=\dfrac{x^3y}{y\cdot\left(x-y\right)^3}\)

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