Basic Math Examples

$(\frac{z}{\sqrt{z} + 7} - \frac{49}{\sqrt{z} + 7}) \cdot 3$

Step 1

Combine the numerators over the common denominator.

$\frac{z - 49}{\sqrt{z} + 7} \cdot 3$

Step 2

Multiply $\frac{z - 49}{\sqrt{z} + 7}$ by $\frac{\sqrt{z} - 7}{\sqrt{z} - 7}$ .

$\frac{z - 49}{\sqrt{z} + 7} \cdot \frac{\sqrt{z} - 7}{\sqrt{z} - 7} \cdot 3$

Step 3

Multiply $\frac{z - 49}{\sqrt{z} + 7}$ by $\frac{\sqrt{z} - 7}{\sqrt{z} - 7}$ .

$\frac{(z - 49) (\sqrt{z} - 7)}{(\sqrt{z} + 7) (\sqrt{z} - 7)} \cdot 3$

Step 4

Expand the denominator using the FOIL method.

$\frac{(z - 49) (\sqrt{z} - 7)}{{\sqrt{z}}^{2} + \sqrt{z} \cdot - 7 + 7 \sqrt{z} - 49} \cdot 3$

Step 5

Simplify.

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Step 5.1

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

$\frac{(z - 49) (\sqrt{z} - 7)}{{(z^{\frac{1}{2}})}^{2} - 49} \cdot 3$

Step 5.2

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

$\frac{(z - 49) (\sqrt{z} - 7)}{z^{\frac{1}{2} \cdot 2} - 49} \cdot 3$

Step 5.3

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

$\frac{(z - 49) (\sqrt{z} - 7)}{z^{\frac{2}{2}} - 49} \cdot 3$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$\frac{(z - 49) (\sqrt{z} - 7)}{z^{\frac{2}{2}} - 49} \cdot 3$

Step 5.4.2

Rewrite the expression.

$\frac{(z - 49) (\sqrt{z} - 7)}{z^{1} - 49} \cdot 3$

Step 5.5

Simplify.

$\frac{(z - 49) (\sqrt{z} - 7)}{z - 49} \cdot 3$

Step 6

Cancel the common factor of $z - 49$ .

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Step 6.1

Cancel the common factor.

$\frac{(z - 49) (\sqrt{z} - 7)}{z - 49} \cdot 3$

Step 6.2

Divide $\sqrt{z} - 7$ by $1$ .

$(\sqrt{z} - 7) \cdot 3$

Step 7

Apply the distributive property.

$\sqrt{z} \cdot 3 - 7 \cdot 3$

Step 8

Simplify the expression.

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Step 8.1

Move $3$ to the left of $\sqrt{z}$ .

$3 \cdot \sqrt{z} - 7 \cdot 3$

Step 8.2

Multiply $- 7$ by $3$ .

$3 \sqrt{z} - 21$