Pre-Algebra Examples

$\frac{3}{n - 4} + \frac{3}{5 n - 6}$

Step 1

To write $\frac{3}{n - 4}$ as a fraction with a common denominator, multiply by $\frac{5 n - 6}{5 n - 6}$ .

$\frac{3}{n - 4} \cdot \frac{5 n - 6}{5 n - 6} + \frac{3}{5 n - 6}$

Step 2

To write $\frac{3}{5 n - 6}$ as a fraction with a common denominator, multiply by $\frac{n - 4}{n - 4}$ .

$\frac{3}{n - 4} \cdot \frac{5 n - 6}{5 n - 6} + \frac{3}{5 n - 6} \cdot \frac{n - 4}{n - 4}$

Step 3

Write each expression with a common denominator of $(n - 4) (5 n - 6)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{n - 4}$ by $\frac{5 n - 6}{5 n - 6}$ .

$\frac{3 (5 n - 6)}{(n - 4) (5 n - 6)} + \frac{3}{5 n - 6} \cdot \frac{n - 4}{n - 4}$

Step 3.2

Multiply $\frac{3}{5 n - 6}$ by $\frac{n - 4}{n - 4}$ .

$\frac{3 (5 n - 6)}{(n - 4) (5 n - 6)} + \frac{3 (n - 4)}{(5 n - 6) (n - 4)}$

Step 3.3

Reorder the factors of $(n - 4) (5 n - 6)$ .

$\frac{3 (5 n - 6)}{(5 n - 6) (n - 4)} + \frac{3 (n - 4)}{(5 n - 6) (n - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (5 n - 6) + 3 (n - 4)}{(5 n - 6) (n - 4)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3$ out of $3 (5 n - 6) + 3 (n - 4)$ .

$\frac{3 (5 n - 6 + n - 4)}{(5 n - 6) (n - 4)}$

Step 5.2

Add $5 n$ and $n$ .

$\frac{3 (6 n - 6 - 4)}{(5 n - 6) (n - 4)}$

Step 5.3

Subtract $4$ from $- 6$ .

$\frac{3 (6 n - 10)}{(5 n - 6) (n - 4)}$

Step 5.4

Factor $2$ out of $6 n - 10$ .

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Step 5.4.1

Factor $2$ out of $6 n$ .

$\frac{3 (2 (3 n) - 10)}{(5 n - 6) (n - 4)}$

Step 5.4.2

Factor $2$ out of $- 10$ .

$\frac{3 (2 (3 n) + 2 (- 5))}{(5 n - 6) (n - 4)}$

Step 5.4.3

Factor $2$ out of $2 (3 n) + 2 (- 5)$ .

$\frac{3 (2 (3 n - 5))}{(5 n - 6) (n - 4)}$

$\frac{3 \cdot 2 (3 n - 5)}{(5 n - 6) (n - 4)}$

Step 5.5

Multiply $3$ by $2$ .

$\frac{6 (3 n - 5)}{(5 n - 6) (n - 4)}$