Algebra Examples

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

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Multiply $\frac{a - 7}{3}$ by $\frac{4}{4}$ .

$\frac{a - 7}{3} \cdot \frac{4}{4} + \frac{5 a - 3}{6} - \frac{2 a + 5}{4}$

Step 1.2

Multiply $\frac{a - 7}{3}$ by $\frac{4}{4}$ .

$\frac{(a - 7) \cdot 4}{3 \cdot 4} + \frac{5 a - 3}{6} - \frac{2 a + 5}{4}$

Step 1.3

Multiply $\frac{5 a - 3}{6}$ by $\frac{2}{2}$ .

$\frac{(a - 7) \cdot 4}{3 \cdot 4} + \frac{5 a - 3}{6} \cdot \frac{2}{2} - \frac{2 a + 5}{4}$

Step 1.4

Multiply $\frac{5 a - 3}{6}$ by $\frac{2}{2}$ .

$\frac{(a - 7) \cdot 4}{3 \cdot 4} + \frac{(5 a - 3) \cdot 2}{6 \cdot 2} - \frac{2 a + 5}{4}$

Step 1.5

Multiply $\frac{2 a + 5}{4}$ by $\frac{3}{3}$ .

$\frac{(a - 7) \cdot 4}{3 \cdot 4} + \frac{(5 a - 3) \cdot 2}{6 \cdot 2} - (\frac{2 a + 5}{4} \cdot \frac{3}{3})$

Step 1.6

Multiply $\frac{2 a + 5}{4}$ by $\frac{3}{3}$ .

$\frac{(a - 7) \cdot 4}{3 \cdot 4} + \frac{(5 a - 3) \cdot 2}{6 \cdot 2} - \frac{(2 a + 5) \cdot 3}{4 \cdot 3}$

Step 1.7

Multiply $3$ by $4$ .

$\frac{(a - 7) \cdot 4}{12} + \frac{(5 a - 3) \cdot 2}{6 \cdot 2} - \frac{(2 a + 5) \cdot 3}{4 \cdot 3}$

Step 1.8

Reorder the factors of $6 \cdot 2$ .

$\frac{(a - 7) \cdot 4}{12} + \frac{(5 a - 3) \cdot 2}{2 \cdot 6} - \frac{(2 a + 5) \cdot 3}{4 \cdot 3}$

Step 1.9

Multiply $2$ by $6$ .

$\frac{(a - 7) \cdot 4}{12} + \frac{(5 a - 3) \cdot 2}{12} - \frac{(2 a + 5) \cdot 3}{4 \cdot 3}$

Step 1.10

Reorder the factors of $4 \cdot 3$ .

$\frac{(a - 7) \cdot 4}{12} + \frac{(5 a - 3) \cdot 2}{12} - \frac{(2 a + 5) \cdot 3}{3 \cdot 4}$

Step 1.11

Multiply $3$ by $4$ .

$\frac{(a - 7) \cdot 4}{12} + \frac{(5 a - 3) \cdot 2}{12} - \frac{(2 a + 5) \cdot 3}{12}$

Step 2

Combine the numerators over the common denominator.

$\frac{(a - 7) \cdot 4 + (5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Apply the distributive property.

$\frac{a \cdot 4 - 7 \cdot 4 + (5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3.2

Move $4$ to the left of $a$ .

$\frac{4 \cdot a - 7 \cdot 4 + (5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3.3

Multiply $- 7$ by $4$ .

$\frac{4 \cdot a - 28 + (5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3.4

Apply the distributive property.

$\frac{4 a - 28 + 5 a \cdot 2 - 3 \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3.5

Multiply $2$ by $5$ .

$\frac{4 a - 28 + 10 a - 3 \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 3.6

Multiply $- 3$ by $2$ .

$\frac{4 a - 28 + 10 a - 6 - (2 a + 5) \cdot 3}{12}$

Step 3.7

Apply the distributive property.

$\frac{4 a - 28 + 10 a - 6 + (- (2 a) - 1 \cdot 5) \cdot 3}{12}$

Step 3.8

Multiply $2$ by $- 1$ .

$\frac{4 a - 28 + 10 a - 6 + (- 2 a - 1 \cdot 5) \cdot 3}{12}$

Step 3.9

Multiply $- 1$ by $5$ .

$\frac{4 a - 28 + 10 a - 6 + (- 2 a - 5) \cdot 3}{12}$

Step 3.10

Apply the distributive property.

$\frac{4 a - 28 + 10 a - 6 - 2 a \cdot 3 - 5 \cdot 3}{12}$

Step 3.11

Multiply $3$ by $- 2$ .

$\frac{4 a - 28 + 10 a - 6 - 6 a - 5 \cdot 3}{12}$

Step 3.12

Multiply $- 5$ by $3$ .

$\frac{4 a - 28 + 10 a - 6 - 6 a - 15}{12}$

Step 4

Simplify by adding terms.

Tap for more steps...

Step 4.1

Add $4 a$ and $10 a$ .

$\frac{14 a - 28 - 6 - 6 a - 15}{12}$

Step 4.2

Subtract $6 a$ from $14 a$ .

$\frac{8 a - 28 - 6 - 15}{12}$

Step 4.3

Simplify by subtracting numbers.

Tap for more steps...

Step 4.3.1

Subtract $6$ from $- 28$ .

$\frac{8 a - 34 - 15}{12}$

Step 4.3.2

Subtract $15$ from $- 34$ .

$\frac{8 a - 49}{12}$