Basic Math Examples

$\frac{4}{g - 3} - \frac{7}{g + 8}$

Step 1

To write $\frac{4}{g - 3}$ as a fraction with a common denominator, multiply by $\frac{g + 8}{g + 8}$ .

$\frac{4}{g - 3} \cdot \frac{g + 8}{g + 8} - \frac{7}{g + 8}$

Step 2

To write $- \frac{7}{g + 8}$ as a fraction with a common denominator, multiply by $\frac{g - 3}{g - 3}$ .

$\frac{4}{g - 3} \cdot \frac{g + 8}{g + 8} - \frac{7}{g + 8} \cdot \frac{g - 3}{g - 3}$

Step 3

Write each expression with a common denominator of $(g - 3) (g + 8)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{g - 3}$ by $\frac{g + 8}{g + 8}$ .

$\frac{4 (g + 8)}{(g - 3) (g + 8)} - \frac{7}{g + 8} \cdot \frac{g - 3}{g - 3}$

Step 3.2

Multiply $\frac{7}{g + 8}$ by $\frac{g - 3}{g - 3}$ .

$\frac{4 (g + 8)}{(g - 3) (g + 8)} - \frac{7 (g - 3)}{(g + 8) (g - 3)}$

Step 3.3

Reorder the factors of $(g - 3) (g + 8)$ .

$\frac{4 (g + 8)}{(g + 8) (g - 3)} - \frac{7 (g - 3)}{(g + 8) (g - 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 (g + 8) - 7 (g - 3)}{(g + 8) (g - 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{4 g + 4 \cdot 8 - 7 (g - 3)}{(g + 8) (g - 3)}$

Step 5.2

Multiply $4$ by $8$ .

$\frac{4 g + 32 - 7 (g - 3)}{(g + 8) (g - 3)}$

Step 5.3

Apply the distributive property.

$\frac{4 g + 32 - 7 g - 7 \cdot - 3}{(g + 8) (g - 3)}$

Step 5.4

Multiply $- 7$ by $- 3$ .

$\frac{4 g + 32 - 7 g + 21}{(g + 8) (g - 3)}$

Step 5.5

Subtract $7 g$ from $4 g$ .

$\frac{- 3 g + 32 + 21}{(g + 8) (g - 3)}$

Step 5.6

Add $32$ and $21$ .

$\frac{- 3 g + 53}{(g + 8) (g - 3)}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 3 g$ .

$\frac{- (3 g) + 53}{(g + 8) (g - 3)}$

Step 6.2

Rewrite $53$ as $- 1 (- 53)$ .

$\frac{- (3 g) - 1 (- 53)}{(g + 8) (g - 3)}$

Step 6.3

Factor $- 1$ out of $- (3 g) - 1 (- 53)$ .

$\frac{- (3 g - 53)}{(g + 8) (g - 3)}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (3 g - 53)$ as $- 1 (3 g - 53)$ .

$\frac{- 1 (3 g - 53)}{(g + 8) (g - 3)}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{3 g - 53}{(g + 8) (g - 3)}$