Algebra Examples

$\frac{3}{8} x - \frac{3}{4} x$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{8}$ and $x$ .

$\frac{3 x}{8} - \frac{3}{4} x$

Step 1.2

Combine $x$ and $\frac{3}{4}$ .

$\frac{3 x}{8} - \frac{x \cdot 3}{4}$

Step 1.3

Move $3$ to the left of $x$ .

$\frac{3 x}{8} - \frac{3 x}{4}$

Step 2

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{8} - \frac{3 x}{4} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 x}{4}$ by $\frac{2}{2}$ .

$\frac{3 x}{8} - \frac{3 x \cdot 2}{4 \cdot 2}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{3 x}{8} - \frac{3 x \cdot 2}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x - 3 x \cdot 2}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3 x$ out of $3 x - 3 x \cdot 2$ .

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Step 5.1.1

Factor $3 x$ out of $3 x$ .

$\frac{3 x (1) - 3 x \cdot 2}{8}$

Step 5.1.2

Factor $3 x$ out of $- 3 x \cdot 2$ .

$\frac{3 x (1) + 3 x (- 1 \cdot 2)}{8}$

Step 5.1.3

Factor $3 x$ out of $3 x (1) + 3 x (- 1 \cdot 2)$ .

$\frac{3 x (1 - 1 \cdot 2)}{8}$

Step 5.2

Multiply $- 1$ by $2$ .

$\frac{3 x (1 - 2)}{8}$

Step 5.3

Subtract $2$ from $1$ .

$\frac{3 x \cdot - 1}{8}$

Step 5.4

Multiply $- 1$ by $3$ .

$\frac{- 3 x}{8}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 x}{8}$