a: \(\frac{35\left(x^2-y^2\right)\left(x+y\right)^2}{77\left(y-x\right)^2\cdot\left(x+y\right)^3}\)
\(=\frac{35\left(x-y\right)\left(x+y\right)\left(x+y\right)^2}{77\cdot\left(x-y\right)^2\cdot\left(x+y\right)^3}=\frac{5}{11\left(x-y\right)}\)
b: \(\frac{4x^2y^2-4xy+1}{8x^3y^3-1-6xy\left(2xy-1\right)}\)
\(=\frac{\left(2xy-1\right)^2}{8x^3y^3-12x^2y^2+6xy-1}\)
\(=\frac{\left(2xy-1\right)^2}{\left(2xy-1\right)^3}=\frac{1}{2xy-1}\)
c: \(\frac{x^2-xy-xz+yz}{x^2+xy-xz-yz}\)
\(=\frac{x\left(x-y\right)-z\left(x-y\right)}{x\left(x+y\right)-z\left(x+y\right)}=\frac{\left(x-y\right)\left(x-z\right)}{\left(x+y\right)\left(x-z\right)}=\frac{x-y}{x+y}\)
d: \(\frac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\)
\(=\frac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}=\frac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}\)
\(=\frac{\left(a+b-c\right)\left(a+b+c\right)}{\left(a+c-b\right)\left(a+c+b\right)}=\frac{a+b-c}{a+c-b}\)
