Question

$$\frac{x}{x-y}+\frac{x}{x+y}+\frac{2xy}{x^{2y}y^{2}$$

Answer

$$2*x^2+2*x^3*y^4$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{2}-y+{x}^{2}+y+2xy{x}^{2}y{y}^{2}\]
Regroup terms.
\[{x}^{2}-y+{x}^{2}+y+2x{x}^{2}yy{y}^{2}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{2}-y+{x}^{2}+y+2{x}^{1+2}{y}^{1+1+2}\]
Simplify  \(1+2\)  to  \(3\).
\[{x}^{2}-y+{x}^{2}+y+2{x}^{3}{y}^{1+3}\]
Simplify  \(1+3\)  to  \(4\).
\[{x}^{2}-y+{x}^{2}+y+2{x}^{3}{y}^{4}\]
Collect like terms.
\[({x}^{2}+{x}^{2})+(-y+y)+2{x}^{3}{y}^{4}\]
Simplify.
\[2{x}^{2}+2{x}^{3}{y}^{4}\]