Basic Math Examples

$\frac{\frac{4}{3 s + 2}}{1 + \frac{0.5 \cdot 4}{3 s + 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{3 s + 2} \cdot \frac{1}{1 + \frac{0.5 \cdot 4}{3 s + 2}}$

Step 2

Multiply $0.5$ by $4$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{1 + \frac{2}{3 s + 2}}$

Step 3

Simplify the denominator.

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Step 3.1

Write $1$ as a fraction with a common denominator.

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{3 s + 2}{3 s + 2} + \frac{2}{3 s + 2}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{3 s + 2 + 2}{3 s + 2}}$

Step 3.3

Rewrite $\frac{3 s + 2 + 2}{3 s + 2}$ in a factored form.

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Step 3.3.1

Add $2$ and $2$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{3 s + 4}{3 s + 2}}$

Step 3.3.2

Factor $1$ out of $3 s + 4$ .

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Step 3.3.2.1

Factor $1$ out of $3 s$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{1 (3 s) + 4}{3 s + 2}}$

Step 3.3.2.2

Rewrite $4$ as $1 (4)$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{1 (3 s) + 1 (4)}{3 s + 2}}$

Step 3.3.2.3

Factor $1$ out of $1 (3 s) + 1 (4)$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{1 (3 s + 4)}{3 s + 2}}$

Step 3.4

Multiply $3 s + 4$ by $1$ .

$\frac{4}{3 s + 2} \cdot \frac{1}{\frac{3 s + 4}{3 s + 2}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{3 s + 2} (1 \frac{3 s + 2}{3 s + 4})$

Step 5

Multiply $\frac{3 s + 2}{3 s + 4}$ by $1$ .

$\frac{4}{3 s + 2} \cdot \frac{3 s + 2}{3 s + 4}$

Step 6

Cancel the common factor of $3 s + 2$ .

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Step 6.1

Cancel the common factor.

$\frac{4}{3 s + 2} \cdot \frac{3 s + 2}{3 s + 4}$

Step 6.2

Rewrite the expression.

$4 \frac{1}{3 s + 4}$

Step 7

Combine $4$ and $\frac{1}{3 s + 4}$ .

$\frac{4}{3 s + 4}$