\(a,=\dfrac{4\left(m-n\right)^2}{5\left(m-n\right)\left(m+n\right)}=\dfrac{4\left(m-n\right)}{5\left(m+n\right)}\\ b,=\dfrac{\left(x-y\right)\left(x-z\right)}{\left(x+y\right)\left(x-z\right)}=\dfrac{x-y}{x+y}\\ c,=\dfrac{\left(x-3\right)\left(y-9\right)}{-\left(x-3\right)}=-\left(y-9\right)=9-y\\ d,=\dfrac{\left(3x+2-x-2\right)\left(3x+2+x+2\right)}{x^2\left(x-1\right)}\\ =\dfrac{2x\left(4x+4\right)}{x^2\left(x-1\right)}=\dfrac{8\left(x+1\right)}{x\left(x-1\right)}\\ e,=\dfrac{\left(y+1\right)\left(y^2+4\right)}{\left(y-3\right)\left(y+1\right)}=\dfrac{y^2+4}{y-3}\\ f,=\dfrac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}=\dfrac{x-4}{x-2}\)
a) \(=\dfrac{2\left(m-n\right)^2}{5\left(m-n\right)\left(m+n\right)}=\dfrac{2\left(m-n\right)}{5\left(m+n\right)}=\dfrac{2m-2n}{5m+5n}\)
b) \(=\dfrac{x\left(x-y\right)-z\left(x-y\right)}{x\left(x+y\right)-z\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-z\right)}{\left(x+y\right)\left(x-z\right)}=\dfrac{x-y}{x+y}\)
c) \(=-\dfrac{y\left(x-3\right)-9\left(x-3\right)}{x-3}=-\dfrac{\left(x-3\right)\left(y-9\right)}{x-3}=9-y\)
d) \(=\dfrac{\left(3x+2-x-2\right)\left(3x+2+x+2\right)}{x^2\left(x-1\right)}=\dfrac{8x\left(x+1\right)}{x^2\left(x-1\right)}=\dfrac{8x+8}{x^2-x}\)
e) \(=\dfrac{y^2\left(y+1\right)+4\left(y+1\right)}{y\left(y-3\right)+\left(y-3\right)}=\dfrac{\left(y+1\right)\left(y^2+4\right)}{\left(y-3\right)\left(y+1\right)}=\dfrac{y^2+4}{y-3}\)
f) \(=\dfrac{x\left(x-4\right)+3\left(x-4\right)}{x\left(x-2\right)+3\left(x-2\right)}=\dfrac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\dfrac{x-4}{x-2}\)
