Bài 1:
a) \(\dfrac{35\left(x^2-y^2\right)\left(x+y\right)^2}{77\left(y-x\right)^2\left(x+y\right)^3}=\dfrac{35\left(x-y\right)\left(x+y\right)^3}{77\left(x-y\right)^2\left(x+y\right)^3}=\dfrac{35}{77\left(x-y\right)}\)
b) \(\dfrac{4x^2y^2+1-4xy}{8x^3y^3-1-6xy\left(2xy-1\right)}=\dfrac{\left(2xy-1\right)^2}{\left(2xy-1\right)\left(4x^2y^2+2xy+1\right)-6xy\left(2xy-1\right)}=\dfrac{\left(2xy-1\right)^2}{\left(2xy-1\right)\left[4x^2y^2+2xy+1-6xy\right]}=\dfrac{2xy-1}{4x^2y^2-4xy+1}=\dfrac{2xy-1}{\left(2xy-1\right)^2}=\dfrac{1}{2xy-1}\)
Bài 2:\(\dfrac{x^2-xy-xz+yz}{x^2+xy-xz-yz}=\dfrac{\left(x^2-xy\right)-\left(xz-yz\right)}{\left(x^2+xy\right)-\left(xz+yz\right)}=\dfrac{x\left(x-y\right)-z\left(x-y\right)}{x\left(x+y\right)-z\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-z\right)}{\left(x+y\right)\left(x-z\right)}=\dfrac{x-y}{x+y}\)
\(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}=\dfrac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}=\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}=\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{\left(a+b+c\right)\left(a-b+c\right)}=\dfrac{a+b-c}{a-b+c}\)
