Algebra Examples

$\frac{\sqrt{a + 3}}{6 - \sqrt{a + 3}}$

Step 1

Multiply $\frac{\sqrt{a + 3}}{6 - \sqrt{a + 3}}$ by $\frac{6 + \sqrt{a + 3}}{6 + \sqrt{a + 3}}$ .

$\frac{\sqrt{a + 3}}{6 - \sqrt{a + 3}} \cdot \frac{6 + \sqrt{a + 3}}{6 + \sqrt{a + 3}}$

Step 2

Multiply $\frac{\sqrt{a + 3}}{6 - \sqrt{a + 3}}$ by $\frac{6 + \sqrt{a + 3}}{6 + \sqrt{a + 3}}$ .

$\frac{\sqrt{a + 3} (6 + \sqrt{a + 3})}{(6 - \sqrt{a + 3}) (6 + \sqrt{a + 3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{a + 3} (6 + \sqrt{a + 3})}{36 + 6 \sqrt{a + 3} - 6 \sqrt{a + 3} - {\sqrt{a + 3}}^{2}}$

Step 4

Simplify.

$\frac{\sqrt{a + 3} (6 + \sqrt{a + 3})}{- a + 33}$

Step 5

Apply the distributive property.

$\frac{\sqrt{a + 3} \cdot 6 + \sqrt{a + 3} \sqrt{a + 3}}{- a + 33}$

Step 6

Move $6$ to the left of $\sqrt{a + 3}$ .

$\frac{6 \cdot \sqrt{a + 3} + \sqrt{a + 3} \sqrt{a + 3}}{- a + 33}$

Step 7

Multiply $\sqrt{a + 3} \sqrt{a + 3}$ .

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Step 7.1

Raise $\sqrt{a + 3}$ to the power of $1$ .

$\frac{6 \cdot \sqrt{a + 3} + {\sqrt{a + 3}}^{1} \sqrt{a + 3}}{- a + 33}$

Step 7.2

Raise $\sqrt{a + 3}$ to the power of $1$ .

$\frac{6 \cdot \sqrt{a + 3} + {\sqrt{a + 3}}^{1} {\sqrt{a + 3}}^{1}}{- a + 33}$

Step 7.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 \cdot \sqrt{a + 3} + {\sqrt{a + 3}}^{1 + 1}}{- a + 33}$

Step 7.4

Add $1$ and $1$ .

$\frac{6 \cdot \sqrt{a + 3} + {\sqrt{a + 3}}^{2}}{- a + 33}$

Step 8

Simplify each term.

$\frac{6 \sqrt{a + 3} + a + 3}{- a + 33}$

Step 9

Simplify with factoring out.

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Step 9.1

Factor $- 1$ out of $- a$ .

$\frac{6 \sqrt{a + 3} + a + 3}{- (a) + 33}$

Step 9.2

Rewrite $33$ as $- 1 (- 33)$ .

$\frac{6 \sqrt{a + 3} + a + 3}{- (a) - 1 (- 33)}$

Step 9.3

Factor $- 1$ out of $- (a) - 1 (- 33)$ .

$\frac{6 \sqrt{a + 3} + a + 3}{- (a - 33)}$

Step 9.4

Rewrite negatives.

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Step 9.4.1

Rewrite $- (a - 33)$ as $- 1 (a - 33)$ .

$\frac{6 \sqrt{a + 3} + a + 3}{- 1 (a - 33)}$

Step 9.4.2

Move the negative in front of the fraction.

$- \frac{6 \sqrt{a + 3} + a + 3}{a - 33}$