Question

Answer 1

a: \(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)

\(=\frac{5x^2-y^2}{xy}-\frac{\left(3x^2-2xy\right)}{xy}\)

\(=\frac{\left(5x^2-y^2-3x^2+2xy\right)}{xy}=\frac{2x^2+2xy-y^2}{xy}\)

b: \(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-y^2}\)

\(=\frac{2x}{x\left(x+2y\right)}+\frac{y}{y\left(x-2y\right)}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\frac{2}{x+2y}+\frac{1}{x-2y}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)

\(=\frac{2\left(x-2y\right)+x+2y+4}{\left(x-2y\right)\left(x+2y\right)}=\frac{3x-2y+4}{\left(x-2y\right)\left(x+2y\right)}\)