Basic Math Examples

$\frac{- 2}{g + 3} - \frac{4}{g - 5}$

Step 1

Move the negative in front of the fraction.

$- \frac{2}{g + 3} - \frac{4}{g - 5}$

Step 2

To write $- \frac{2}{g + 3}$ as a fraction with a common denominator, multiply by $\frac{g - 5}{g - 5}$ .

$- \frac{2}{g + 3} \cdot \frac{g - 5}{g - 5} - \frac{4}{g - 5}$

Step 3

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

$- \frac{2}{g + 3} \cdot \frac{g - 5}{g - 5} - \frac{4}{g - 5} \cdot \frac{g + 3}{g + 3}$

Step 4

Write each expression with a common denominator of $(g + 3) (g - 5)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{g + 3}$ by $\frac{g - 5}{g - 5}$ .

$- \frac{2 (g - 5)}{(g + 3) (g - 5)} - \frac{4}{g - 5} \cdot \frac{g + 3}{g + 3}$

Step 4.2

Multiply $\frac{4}{g - 5}$ by $\frac{g + 3}{g + 3}$ .

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

Step 4.3

Reorder the factors of $(g - 5) (g + 3)$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Factor $- 2$ out of $- 2 (g - 5) - 4 (g + 3)$ .

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Step 6.1.1

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

$\frac{- 2 (g - 5) - 2 (2 (g + 3))}{(g + 3) (g - 5)}$

Step 6.1.2

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

$\frac{- 2 (g - 5 + 2 (g + 3))}{(g + 3) (g - 5)}$

Step 6.2

Apply the distributive property.

$\frac{- 2 (g - 5 + 2 g + 2 \cdot 3)}{(g + 3) (g - 5)}$

Step 6.3

Multiply $2$ by $3$ .

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

Step 6.4

Add $g$ and $2 g$ .

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

Step 6.5

Add $- 5$ and $6$ .

$\frac{- 2 (3 g + 1)}{(g + 3) (g - 5)}$

Step 7

Move the negative in front of the fraction.

$- \frac{2 (3 g + 1)}{(g + 3) (g - 5)}$