Question

Rút gọn các phân thức :

a, \(\dfrac{ax+ay-bx-by}{ax-ay-bx+by}\)

b, \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\)

Answer 1

a) \(\dfrac{ax+ay-bx-by}{ax-ay-bx+by}=\dfrac{a\left(x+y\right)-b\left(x+y\right)}{a\left(x-y\right)-b\left(x-y\right)}=\dfrac{\left(a-b\right)\left(x+y\right)}{\left(a-b\right)\left(x-y\right)}=\dfrac{x+y}{x-y}\)

b) \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}=\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}=\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{\left(a+c+b\right)\left(a+c-b\right)}=\dfrac{a+b-c}{a+c-b}\)