Algebra Examples

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

Step 1

To write $\frac{a - 7}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Multiply $\frac{a - 7}{3}$ by $\frac{2}{2}$ .

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

Step 2.2

Multiply $3$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

To write $\frac{(a - 7) \cdot 2 + 5 a - 3}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 5

To write $- \frac{2 a + 5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

Multiply $6$ by $2$ .

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

Step 6.3

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

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

Step 6.4

Multiply $4$ by $3$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Rewrite $\frac{((a - 7) \cdot 2 + 5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$ in a factored form.

Tap for more steps...

Step 8.1

Simplify each term.

Tap for more steps...

Step 8.1.1

Apply the distributive property.

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

Step 8.1.2

Move $2$ to the left of $a$ .

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

Step 8.1.3

Multiply $- 7$ by $2$ .

$\frac{(2 a - 14 + 5 a - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 8.2

Add $2 a$ and $5 a$ .

$\frac{(7 a - 14 - 3) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 8.3

Subtract $3$ from $- 14$ .

$\frac{(7 a - 17) \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 8.4

Apply the distributive property.

$\frac{7 a \cdot 2 - 17 \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 8.5

Multiply $2$ by $7$ .

$\frac{14 a - 17 \cdot 2 - (2 a + 5) \cdot 3}{12}$

Step 8.6

Multiply $- 17$ by $2$ .

$\frac{14 a - 34 - (2 a + 5) \cdot 3}{12}$

Step 8.7

Apply the distributive property.

$\frac{14 a - 34 + (- (2 a) - 1 \cdot 5) \cdot 3}{12}$

Step 8.8

Multiply $2$ by $- 1$ .

$\frac{14 a - 34 + (- 2 a - 1 \cdot 5) \cdot 3}{12}$

Step 8.9

Multiply $- 1$ by $5$ .

$\frac{14 a - 34 + (- 2 a - 5) \cdot 3}{12}$

Step 8.10

Apply the distributive property.

$\frac{14 a - 34 - 2 a \cdot 3 - 5 \cdot 3}{12}$

Step 8.11

Multiply $3$ by $- 2$ .

$\frac{14 a - 34 - 6 a - 5 \cdot 3}{12}$

Step 8.12

Multiply $- 5$ by $3$ .

$\frac{14 a - 34 - 6 a - 15}{12}$

Step 8.13

Subtract $6 a$ from $14 a$ .

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

Step 8.14

Subtract $15$ from $- 34$ .

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