Algebra Examples

$\frac{5}{6} x - \frac{5}{12} x - \frac{1}{3} + \frac{1}{4} x + \frac{1}{12}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} - \frac{5}{12} x - \frac{1}{3} + \frac{1}{4} x + \frac{1}{12}$

Step 1.2

Combine $x$ and $\frac{5}{12}$ .

$\frac{5 x}{6} - \frac{x \cdot 5}{12} - \frac{1}{3} + \frac{1}{4} x + \frac{1}{12}$

Step 1.3

Move $5$ to the left of $x$ .

$\frac{5 x}{6} - \frac{5 \cdot x}{12} - \frac{1}{3} + \frac{1}{4} x + \frac{1}{12}$

Step 1.4

Combine $\frac{1}{4}$ and $x$ .

$\frac{5 x}{6} - \frac{5 x}{12} - \frac{1}{3} + \frac{x}{4} + \frac{1}{12}$

Step 2

To write $\frac{5 x}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{6} \cdot \frac{2}{2} - \frac{5 x}{12} - \frac{1}{3} + \frac{x}{4} + \frac{1}{12}$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 x}{6}$ by $\frac{2}{2}$ .

$\frac{5 x \cdot 2}{6 \cdot 2} - \frac{5 x}{12} - \frac{1}{3} + \frac{x}{4} + \frac{1}{12}$

Step 3.2

Multiply $6$ by $2$ .

$\frac{5 x \cdot 2}{12} - \frac{5 x}{12} - \frac{1}{3} + \frac{x}{4} + \frac{1}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 - 5 x}{12} - \frac{1}{3} + \frac{x}{4} + \frac{1}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 - 5 x + 1}{12} + \frac{- 1}{3} + \frac{x}{4}$

Step 6

Multiply $2$ by $5$ .

$\frac{10 x - 5 x + 1}{12} + \frac{- 1}{3} + \frac{x}{4}$

Step 7

Subtract $5 x$ from $10 x$ .

$\frac{5 x + 1}{12} + \frac{- 1}{3} + \frac{x}{4}$

Step 8

Move the negative in front of the fraction.

$\frac{5 x + 1}{12} - \frac{1}{3} + \frac{x}{4}$

Step 9

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x + 1}{12} - \frac{1}{3} \cdot \frac{4}{4} + \frac{x}{4}$

Step 10

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 10.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{5 x + 1}{12} - \frac{4}{3 \cdot 4} + \frac{x}{4}$

Step 10.2

Multiply $3$ by $4$ .

$\frac{5 x + 1}{12} - \frac{4}{12} + \frac{x}{4}$

Step 11

Combine the numerators over the common denominator.

$\frac{5 x + 1 - 4}{12} + \frac{x}{4}$

Step 12

Subtract $4$ from $1$ .

$\frac{5 x - 3}{12} + \frac{x}{4}$

Step 13

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

$\frac{5 x - 3}{12} + \frac{x}{4} \cdot \frac{3}{3}$

Step 14

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 14.1

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

$\frac{5 x - 3}{12} + \frac{x \cdot 3}{4 \cdot 3}$

Step 14.2

Multiply $4$ by $3$ .

$\frac{5 x - 3}{12} + \frac{x \cdot 3}{12}$

Step 15

Combine the numerators over the common denominator.

$\frac{5 x - 3 + x \cdot 3}{12}$

Step 16

Simplify the numerator.

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Step 16.1

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

$\frac{5 x - 3 + 3 \cdot x}{12}$

Step 16.2

Add $5 x$ and $3 x$ .

$\frac{8 x - 3}{12}$