Algebra Examples

$\frac{- 2}{3 x} - \frac{1}{2}$

Move the negative in front of the fraction.

$- \frac{2}{3 x} - \frac{1}{2}$

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

$- \frac{2}{3 x} \frac{2}{2} - \frac{1}{2}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$- \frac{2}{3 x} \frac{2}{2} - \frac{1}{2} \frac{3 x}{3 x}$

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$- \frac{2 \cdot 2}{3 x \cdot 2} - \frac{1}{2} \frac{3 x}{3 x}$

Multiply $2$ by $3$ to get $6$ .

$- \frac{2 \cdot 2}{6 x} - \frac{1}{2} \frac{3 x}{3 x}$

Combine.

$- \frac{2 \cdot 2}{6 x} - \frac{1 (3 x)}{2 (3 x)}$

Multiply $3$ by $2$ to get $6$ .

$- \frac{2 \cdot 2}{6 x} - \frac{1 (3 x)}{6 x}$

Combine the numerators over the common denominator.

$\frac{- (2 \cdot 2) - (1 (3 x))}{6 x}$

Simplify the numerator.

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Multiply $2$ by $2$ to get $4$ .

$\frac{- 1 \cdot 4 - (1 (3 x))}{6 x}$

Multiply $- 1$ by $4$ to get $- 4$ .

$\frac{- 4 - (1 (3 x))}{6 x}$

Multiply $3 x$ by $1$ to get $3 x$ .

$\frac{- 4 - (3 x)}{6 x}$

Multiply $3$ by $- 1$ to get $- 3$ .

$\frac{- 4 - 3 x}{6 x}$

Simplify with factoring out.

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Reorder $- 4$ and $- 3 x$ .

$\frac{- 3 x - 4}{6 x}$

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

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

$\frac{- 1 (3) x - 4}{6 x}$

Move $- 1$ .

$\frac{- ((3) x) - 4}{6 x}$

Multiply $3$ by $x$ to get $3 x$ .

$\frac{- (3 x) - 4}{6 x}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- (3 x) - 1 (4)}{6 x}$

Factor $- 1$ out of $- (3 x) - 1 (4)$ .

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

Simplify the expression.

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Rewrite $- (3 x + 4)$ as $- 1 (3 x + 4)$ .

$\frac{- 1 (3 x + 4)}{6 x}$

Move the negative in front of the fraction.

$- \frac{3 x + 4}{6 x}$

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