Simplify (x^2-w^2)/(x^3-w^3)*(x^2+xw+w^2)/(x^2+2xw+w^2)

$\frac{x^{2} - w^{2}}{x^{3} - w^{3}} \cdot \frac{x^{2} + x w + w^{2}}{x^{2} + 2 x w + w^{2}}$

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 $b = w$ .

$\frac{(x + w) (x - w)}{x^{3} - w^{3}} \cdot \frac{x^{2} + x w + w^{2}}{x^{2} + 2 x w + w^{2}}$

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 $b = w$ .

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

Factor using the perfect square rule.

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Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot w$

Simplify.

$2 a b = 2 x w$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = w$ .

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

Simplify terms.

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Cancel the common factor of $x + w$ .

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Factor $x + w$ out of ${(x + w)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{2} + x w + w^{2}$ .

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Factor $x^{2} + x w + w^{2}$ out of $(x - w) (x^{2} + x w + w^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - w}{x - w} \cdot \frac{1}{x + w}$

Multiply $\frac{x - w}{x - w}$ and $\frac{1}{x + w}$ .

$\frac{x - w}{(x - w) (x + w)}$

Cancel the common factor of $x - w$ .

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Cancel the common factor.

$\frac{x - w}{(x - w) (x + w)}$

Rewrite the expression.

$\frac{1}{x + w}$

Simplify (x^2-w^2)/(x^3-w^3)*(x^2+xw+w^2)/(x^2+2xw+w^2)