Basic Math Examples

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

Step 1

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{6 a}{6 a}$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine $- 3$ and $\frac{6 a}{6 a}$ .

$\frac{- 3 (6 a)}{6 a} + \frac{3 a + 4 y}{6 a} + \frac{a + 2 y}{4 a}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{- 3 (6 a) + 3 a + 4 y}{6 a} + \frac{a + 2 y}{4 a}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $- 3$ by $6$ .

$\frac{- 18 a + 3 a + 4 y}{6 a} + \frac{a + 2 y}{4 a}$

Step 3.2

Add $- 18 a$ and $3 a$ .

$\frac{- 15 a + 4 y}{6 a} + \frac{a + 2 y}{4 a}$

Step 4

To write $\frac{- 15 a + 4 y}{6 a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 15 a + 4 y}{6 a} \cdot \frac{2}{2} + \frac{a + 2 y}{4 a}$

Step 5

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

$\frac{- 15 a + 4 y}{6 a} \cdot \frac{2}{2} + \frac{a + 2 y}{4 a} \cdot \frac{3}{3}$

Step 6

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

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Step 6.1

Multiply $\frac{- 15 a + 4 y}{6 a}$ by $\frac{2}{2}$ .

$\frac{(- 15 a + 4 y) \cdot 2}{6 a \cdot 2} + \frac{a + 2 y}{4 a} \cdot \frac{3}{3}$

Step 6.2

Multiply $2$ by $6$ .

$\frac{(- 15 a + 4 y) \cdot 2}{12 a} + \frac{a + 2 y}{4 a} \cdot \frac{3}{3}$

Step 6.3

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

$\frac{(- 15 a + 4 y) \cdot 2}{12 a} + \frac{(a + 2 y) \cdot 3}{4 a \cdot 3}$

Step 6.4

Multiply $3$ by $4$ .

$\frac{(- 15 a + 4 y) \cdot 2}{12 a} + \frac{(a + 2 y) \cdot 3}{12 a}$

Step 7

Combine the numerators over the common denominator.

$\frac{(- 15 a + 4 y) \cdot 2 + (a + 2 y) \cdot 3}{12 a}$

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{- 15 a \cdot 2 + 4 y \cdot 2 + (a + 2 y) \cdot 3}{12 a}$

Step 8.2

Multiply $2$ by $- 15$ .

$\frac{- 30 a + 4 y \cdot 2 + (a + 2 y) \cdot 3}{12 a}$

Step 8.3

Multiply $2$ by $4$ .

$\frac{- 30 a + 8 y + (a + 2 y) \cdot 3}{12 a}$

Step 8.4

Apply the distributive property.

$\frac{- 30 a + 8 y + a \cdot 3 + 2 y \cdot 3}{12 a}$

Step 8.5

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

$\frac{- 30 a + 8 y + 3 \cdot a + 2 y \cdot 3}{12 a}$

Step 8.6

Multiply $3$ by $2$ .

$\frac{- 30 a + 8 y + 3 \cdot a + 6 y}{12 a}$

Step 8.7

Add $- 30 a$ and $3 a$ .

$\frac{- 27 a + 8 y + 6 y}{12 a}$

Step 8.8

Add $8 y$ and $6 y$ .

$\frac{- 27 a + 14 y}{12 a}$

Step 9

Simplify with factoring out.

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Step 9.1

Factor $- 1$ out of $- 27 a$ .

$\frac{- (27 a) + 14 y}{12 a}$

Step 9.2

Factor $- 1$ out of $14 y$ .

$\frac{- (27 a) - (- 14 y)}{12 a}$

Step 9.3

Factor $- 1$ out of $- (27 a) - (- 14 y)$ .

$\frac{- (27 a - 14 y)}{12 a}$

Step 9.4

Simplify the expression.

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Step 9.4.1

Rewrite $- (27 a - 14 y)$ as $- 1 (27 a - 14 y)$ .

$\frac{- 1 (27 a - 14 y)}{12 a}$

Step 9.4.2

Move the negative in front of the fraction.

$- \frac{27 a - 14 y}{12 a}$