Simplify (x^2-y^2)/(x^3-y^3)

$\frac{x^{2} - y^{2}}{x^{3} - y^{3}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$\frac{(x + y) (x - y)}{x^{3} - y^{3}}$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = y$ .

$\frac{(x + y) (x - y)}{(x - y) (x^{2} + x y + y^{2})}$

Cancel the common factor of $x - y$ .

Cancel the common factor.

$\frac{(x + y) (x - y)}{(x - y) (x^{2} + x y + y^{2})}$

Rewrite the expression.

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

Simplify (x^2-y^2)/(x^3-y^3)

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