Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

Simplify.

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Step 1.2.1

Add $x$ and $x$ .

$\frac{(h + 2 x) (x + h - x)}{h}$

Step 1.2.2

Subtract $x$ from $x$ .

$\frac{(h + 2 x) (h + 0)}{h}$

Step 1.2.3

Add $h$ and $0$ .

$\frac{(h + 2 x) h}{h}$

Step 2

Cancel the common factor of $h$ .

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Step 2.1

Cancel the common factor.

$\frac{(h + 2 x) h}{h}$

Step 2.2

Divide $h + 2 x$ by $1$ .

$h + 2 x$