Pre-Algebra Examples

$\frac{\frac{\frac{g + 3}{2 g - 1}}{g^{2} + 3 g}}{4 g + 2}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{g + 3}{2 g - 1}}{g^{2} + 3 g} \cdot \frac{1}{4 g + 2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{g + 3}{2 g - 1} \cdot \frac{1}{g^{2} + 3 g} \frac{1}{4 g + 2}$

Step 3

Factor $g$ out of $g^{2} + 3 g$ .

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Step 3.1

Factor $g$ out of $g^{2}$ .

$\frac{g + 3}{2 g - 1} \cdot \frac{1}{g \cdot g + 3 g} \frac{1}{4 g + 2}$

Step 3.2

Factor $g$ out of $3 g$ .

$\frac{g + 3}{2 g - 1} \cdot \frac{1}{g \cdot g + g \cdot 3} \frac{1}{4 g + 2}$

Step 3.3

Factor $g$ out of $g \cdot g + g \cdot 3$ .

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

Step 4

Cancel the common factor of $g + 3$ .

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Step 4.1

Factor $g + 3$ out of $g (g + 3)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{1}{2 g - 1} \cdot \frac{1}{g} \frac{1}{4 g + 2}$

Step 5

Multiply $\frac{1}{2 g - 1}$ by $\frac{1}{g}$ .

$\frac{1}{(2 g - 1) g} \cdot \frac{1}{4 g + 2}$

Step 6

Factor $2$ out of $4 g + 2$ .

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Step 6.1

Factor $2$ out of $4 g$ .

$\frac{1}{(2 g - 1) g} \cdot \frac{1}{2 (2 g) + 2}$

Step 6.2

Factor $2$ out of $2$ .

$\frac{1}{(2 g - 1) g} \cdot \frac{1}{2 (2 g) + 2 (1)}$

Step 6.3

Factor $2$ out of $2 (2 g) + 2 (1)$ .

$\frac{1}{(2 g - 1) g} \cdot \frac{1}{2 (2 g + 1)}$

Step 7

Multiply $\frac{1}{(2 g - 1) g}$ by $\frac{1}{2 (2 g + 1)}$ .

$\frac{1}{(2 g - 1) g (2 (2 g + 1))}$

Step 8

Move $2$ to the left of $(2 g - 1) g$ .

$\frac{1}{2 \cdot ((2 g - 1) g) (2 g + 1)}$

Step 9

Reorder factors in $\frac{1}{2 (2 g - 1) g (2 g + 1)}$ .

$\frac{1}{2 g (2 g - 1) (2 g + 1)}$