Question

Rút gọn phân thức :

a, \(\dfrac{xy+1-x-y}{y+z-1-yz}\)

b, \(\dfrac{a^2-b^2}{a^2-a-b-b^2}\)

c, \(\dfrac{a^3+1}{2a^2+4a+2}\)

Answer 1

a: \(=\dfrac{x\left(y-1\right)-\left(y-1\right)}{y\left(1-z\right)-\left(1-z\right)}=\dfrac{\left(y-1\right)\left(x-1\right)}{\left(1-z\right)\left(y-1\right)}=\dfrac{x-1}{1-z}\)

b: \(=\dfrac{\left(a-b\right)\left(a+b\right)}{\left(a-b\right)\left(a+b\right)-\left(a+b\right)}=\dfrac{a-b}{a-b-1}\)

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