Algebra Examples

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

Step 1

To write $x$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Factor $x$ out of $x y^{2} - x$ .

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Step 3.1.1

Factor $x$ out of $x y^{2}$ .

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

Step 3.1.2

Factor $x$ out of $- x$ .

$\frac{x (y^{2}) + x \cdot - 1}{y^{2}}$

Step 3.1.3

Factor $x$ out of $x (y^{2}) + x \cdot - 1$ .

$\frac{x (y^{2} - 1)}{y^{2}}$

Step 3.2

Rewrite $1$ as $1^{2}$ .

$\frac{x (y^{2} - 1^{2})}{y^{2}}$

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 1$ .

$\frac{x (y + 1) (y - 1)}{y^{2}}$