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

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

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

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

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 $b = y$ .

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

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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