1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$- \frac { \frac { 1 } { 6 } + \frac { 7 } { 12 } 0 / \frac { 3 } { 7 } } { \frac { 2 } { 3 } \times \frac { 3 } { 4 } - \frac { 2 } { 3 } \div \frac { 5 } { 7 } }$$

Evaluate

$\frac{5}{13}\approx 0.384615385$

Solution Steps

Multiply $\frac{7}{12}$ and $0$ to get $0$.

$$-\frac{\frac{1}{6}+\frac{0}{\frac{3}{7}}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Zero divided by any non-zero number gives zero.

$$-\frac{\frac{1}{6}+0}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Add $\frac{1}{6}$ and $0$ to get $\frac{1}{6}$.

$$-\frac{\frac{1}{6}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Multiply $\frac{2}{3}$ times $\frac{3}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{\frac{1}{6}}{\frac{2\times 3}{3\times 4}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Cancel out $3$ in both numerator and denominator.

$$-\frac{\frac{1}{6}}{\frac{2}{4}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{\frac{1}{6}}{\frac{1}{2}-\frac{\frac{2}{3}}{\frac{5}{7}}}$$

Divide $\frac{2}{3}$ by $\frac{5}{7}$ by multiplying $\frac{2}{3}$ by the reciprocal of $\frac{5}{7}$.

$$-\frac{\frac{1}{6}}{\frac{1}{2}-\frac{2}{3}\times \frac{7}{5}}$$

Multiply $\frac{2}{3}$ times $\frac{7}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{\frac{1}{6}}{\frac{1}{2}-\frac{2\times 7}{3\times 5}}$$

Do the multiplications in the fraction $\frac{2\times 7}{3\times 5}$.

$$-\frac{\frac{1}{6}}{\frac{1}{2}-\frac{14}{15}}$$

Least common multiple of $2$ and $15$ is $30$. Convert $\frac{1}{2}$ and $\frac{14}{15}$ to fractions with denominator $30$.

$$-\frac{\frac{1}{6}}{\frac{15}{30}-\frac{28}{30}}$$

Since $\frac{15}{30}$ and $\frac{28}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{\frac{1}{6}}{\frac{15-28}{30}}$$

Subtract $28$ from $15$ to get $-13$.

$$-\frac{\frac{1}{6}}{-\frac{13}{30}}$$

Divide $\frac{1}{6}$ by $-\frac{13}{30}$ by multiplying $\frac{1}{6}$ by the reciprocal of $-\frac{13}{30}$.

$$-\frac{1}{6}\left(-\frac{30}{13}\right)$$

Multiply $\frac{1}{6}$ times $-\frac{30}{13}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1\left(-30\right)}{6\times 13}$$

Do the multiplications in the fraction $\frac{1\left(-30\right)}{6\times 13}$.

$$-\frac{-30}{78}$$

Reduce the fraction $\frac{-30}{78}$ to lowest terms by extracting and canceling out $6$.

$$-\left(-\frac{5}{13}\right)$$

The opposite of $-\frac{5}{13}$ is $\frac{5}{13}$.

$$\frac{5}{13}$$

Show Solution

Factor

$\frac{5}{13} = 0.38461538461538464$

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