Basic Math Examples

$\frac{6}{w + 4} + \frac{4}{w - 1}$

Step 1

To write $\frac{6}{w + 4}$ as a fraction with a common denominator, multiply by $\frac{w - 1}{w - 1}$ .

$\frac{6}{w + 4} \cdot \frac{w - 1}{w - 1} + \frac{4}{w - 1}$

Step 2

To write $\frac{4}{w - 1}$ as a fraction with a common denominator, multiply by $\frac{w + 4}{w + 4}$ .

$\frac{6}{w + 4} \cdot \frac{w - 1}{w - 1} + \frac{4}{w - 1} \cdot \frac{w + 4}{w + 4}$

Step 3

Write each expression with a common denominator of $(w + 4) (w - 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{w + 4}$ by $\frac{w - 1}{w - 1}$ .

$\frac{6 (w - 1)}{(w + 4) (w - 1)} + \frac{4}{w - 1} \cdot \frac{w + 4}{w + 4}$

Step 3.2

Multiply $\frac{4}{w - 1}$ by $\frac{w + 4}{w + 4}$ .

$\frac{6 (w - 1)}{(w + 4) (w - 1)} + \frac{4 (w + 4)}{(w - 1) (w + 4)}$

Step 3.3

Reorder the factors of $(w - 1) (w + 4)$ .

$\frac{6 (w - 1)}{(w + 4) (w - 1)} + \frac{4 (w + 4)}{(w + 4) (w - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (w - 1) + 4 (w + 4)}{(w + 4) (w - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $2$ out of $6 (w - 1) + 4 (w + 4)$ .

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Step 5.1.1

Factor $2$ out of $6 (w - 1)$ .

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

Step 5.1.2

Factor $2$ out of $4 (w + 4)$ .

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

Step 5.1.3

Factor $2$ out of $2 (3 (w - 1)) + 2 (2 (w + 4))$ .

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Multiply $3$ by $- 1$ .

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

Step 5.4

Apply the distributive property.

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

Step 5.5

Multiply $2$ by $4$ .

$\frac{2 (3 w - 3 + 2 w + 8)}{(w + 4) (w - 1)}$

Step 5.6

Add $3 w$ and $2 w$ .

$\frac{2 (5 w - 3 + 8)}{(w + 4) (w - 1)}$

Step 5.7

Add $- 3$ and $8$ .

$\frac{2 (5 w + 5)}{(w + 4) (w - 1)}$

Step 5.8

Factor $5$ out of $5 w + 5$ .

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Step 5.8.1

Factor $5$ out of $5 w$ .

$\frac{2 (5 (w) + 5)}{(w + 4) (w - 1)}$

Step 5.8.2

Factor $5$ out of $5$ .

$\frac{2 (5 (w) + 5 (1))}{(w + 4) (w - 1)}$

Step 5.8.3

Factor $5$ out of $5 (w) + 5 (1)$ .

$\frac{2 (5 (w + 1))}{(w + 4) (w - 1)}$

$\frac{2 \cdot 5 (w + 1)}{(w + 4) (w - 1)}$

Step 5.9

Multiply $2$ by $5$ .

$\frac{10 (w + 1)}{(w + 4) (w - 1)}$