Simplify -8/(15g^2)+-7/(20g)

$\frac{- 8}{15 g^{2}} + \frac{- 7}{20 g}$

Step 1

Simplify each term.

Move the negative in front of the fraction.

$- \frac{8}{15 g^{2}} + \frac{- 7}{20 g}$

Move the negative in front of the fraction.

$- \frac{8}{15 g^{2}} - \frac{7}{20 g}$

Step 2

To write $- \frac{8}{15 g^{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{8}{15 g^{2}} \cdot \frac{4}{4} - \frac{7}{20 g}$

Step 3

To write $- \frac{7}{20 g}$ as a fraction with a common denominator, multiply by $\frac{3 g}{3 g}$ .

$- \frac{8}{15 g^{2}} \cdot \frac{4}{4} - \frac{7}{20 g} \cdot \frac{3 g}{3 g}$

Step 4

Write each expression with a common denominator of $60 g^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{15 g^{2}}$ by $\frac{4}{4}$ .

$- \frac{8 \cdot 4}{15 g^{2} \cdot 4} - \frac{7}{20 g} \cdot \frac{3 g}{3 g}$

Multiply $4$ by $15$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7}{20 g} \cdot \frac{3 g}{3 g}$

Multiply $\frac{7}{20 g}$ by $\frac{3 g}{3 g}$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{20 g (3 g)}$

Multiply $3$ by $20$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{60 g \cdot g}$

Raise $g$ to the power of $1$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{60 (g^{1} g)}$

Raise $g$ to the power of $1$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{60 (g^{1} g^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{60 g^{1 + 1}}$

Add $1$ and $1$ .

$- \frac{8 \cdot 4}{60 g^{2}} - \frac{7 (3 g)}{60 g^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 4 - 7 (3 g)}{60 g^{2}}$

Step 6

Simplify the numerator.

Multiply $- 8$ by $4$ .

$\frac{- 32 - 7 \cdot 3 g}{60 g^{2}}$

Multiply $- 7$ by $3$ .

$\frac{- 32 - 21 g}{60 g^{2}}$

Step 7

Simplify with factoring out.

Rewrite $- 32$ as $- 1 (32)$ .

$\frac{- 1 (32) - 21 g}{60 g^{2}}$

Factor $- 1$ out of $- 21 g$ .

$\frac{- 1 (32) - (21 g)}{60 g^{2}}$

Factor $- 1$ out of $- 1 (32) - (21 g)$ .

$\frac{- 1 (32 + 21 g)}{60 g^{2}}$

Move the negative in front of the fraction.

$- \frac{32 + 21 g}{60 g^{2}}$

Simplify -8/(15g^2)+-7/(20g)

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