Basic Math Examples

$\frac{- 8}{\sqrt{y} + 4}$

Step 1

Move the negative in front of the fraction.

$- \frac{8}{\sqrt{y} + 4}$

Step 2

Multiply $\frac{8}{\sqrt{y} + 4}$ by $\frac{\sqrt{y} - 4}{\sqrt{y} - 4}$ .

$- (\frac{8}{\sqrt{y} + 4} \cdot \frac{\sqrt{y} - 4}{\sqrt{y} - 4})$

Step 3

Multiply $\frac{8}{\sqrt{y} + 4}$ by $\frac{\sqrt{y} - 4}{\sqrt{y} - 4}$ .

$- \frac{8 (\sqrt{y} - 4)}{(\sqrt{y} + 4) (\sqrt{y} - 4)}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{8 (\sqrt{y} - 4)}{{\sqrt{y}}^{2} + \sqrt{y} \cdot - 4 + 4 \sqrt{y} - 16}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$- \frac{8 (\sqrt{y} - 4)}{{(y^{\frac{1}{2}})}^{2} - 16}$

Step 5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{8 (\sqrt{y} - 4)}{y^{\frac{1}{2} \cdot 2} - 16}$

Step 5.3

Combine $\frac{1}{2}$ and $2$ .

$- \frac{8 (\sqrt{y} - 4)}{y^{\frac{2}{2}} - 16}$

Step 5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.4.1

Cancel the common factor.

$- \frac{8 (\sqrt{y} - 4)}{y^{\frac{2}{2}} - 16}$

Step 5.4.2

Rewrite the expression.

$- \frac{8 (\sqrt{y} - 4)}{y^{1} - 16}$

Step 5.5

Simplify.

$- \frac{8 (\sqrt{y} - 4)}{y - 16}$