Question

Rút gọn phân thức: 

a) \(\dfrac{6x^2y^2}{8xy^5}\)          b) \(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\) 

c) \(\dfrac{2x^2+2x}{x+1}\)      d) \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

Answer 1

a)\(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)

b)\(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}=\dfrac{2y}{3\left(x+y\right)^2}\)

c)\(\dfrac{2x^2+2x}{x+1}=\dfrac{2x\left(x+1\right)}{x+1}=2x\)

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

Answer 2

a)

\(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)

b) 

\(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}=\dfrac{2y}{3\left(x+y\right)^2}\)

c)

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

d)

\(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)

Answer 3

\(a)\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)

\(b)\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}=\dfrac{2y}{3\left(x+y\right)^2}\)

\(c)\dfrac{2x^2+2x}{x+1}=\dfrac{2x\left(x+1\right)}{x+1}=2x\)

\(d)\dfrac{x^2-xy-x+y}{x^2+xy-x-y}=\dfrac{\left(x^2-x\right)-\left(xy-y\right)}{\left(x^2-x\right)+\left(xy-y\right)}=\dfrac{x\left(x-1\right)-y\left(x-1\right)}{x\left(x-1\right)+y\left(x-1\right)}=\dfrac{\left(x-1\right)\left(x-y\right)}{\left(x-1\right)\left(x+y\right)}=\dfrac{x-y}{x+y}\)