<s>[INST] Basic Algebra combining exponent fractions/simplifying (George F Simmons "Precalculus in Nutshell") From George F. Simmons 'Precalculus' book, Algebra section, 5(d);
Combine and Simplify 
$$\frac{x}{xy^2} + \frac{y}{x^2y}$$
Combine:
= $$\frac{x(x^2y) + y(xy^2)}{(xy^2)(x^2y)}$$
Simplify: = $$\frac{x(x^2y) + y(xy^2)}{xy(x^2y^2)}$$ 
The given answer, which I can't figure out how he arrives at it is: $$\frac{x^2 +y^2}{x^2y^2}$$
 [/INST] $$\frac{x}{xy^2}+\frac{y}{x^2y}=\frac{x}{x}\cdot\frac{x}{xy^2}+\frac{y}{y}\cdot\frac{y}{x^2y}=\frac{x\cdot x}{xy^2\cdot x}+\frac{y\cdot y}{x^2y\cdot y}=\frac{x^2}{x^2y^2}+\frac{y^2}{x^2y^2}=\frac{x^2+y^2}{x^2y^2}$$
</s>