Algebra Examples

$3 - \frac{2 x - y}{4} + \frac{x + 4 y}{12}$

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Multiply $3$ by $4$ .

$\frac{12 - (2 x - y)}{4} + \frac{x + 4 y}{12}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{12 - (2 x) - - y}{4} + \frac{x + 4 y}{12}$

Step 3.2

Multiply $2$ by $- 1$ .

$\frac{12 - 2 x - - y}{4} + \frac{x + 4 y}{12}$

Step 3.3

Multiply $- - y$ .

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Step 3.3.1

Multiply $- 1$ by $- 1$ .

$\frac{12 - 2 x + 1 y}{4} + \frac{x + 4 y}{12}$

Step 3.3.2

Multiply $y$ by $1$ .

$\frac{12 - 2 x + y}{4} + \frac{x + 4 y}{12}$

Step 4

To write $\frac{12 - 2 x + y}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

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

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Step 5.1

Multiply $\frac{12 - 2 x + y}{4}$ by $\frac{3}{3}$ .

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

Step 5.2

Multiply $4$ by $3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

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

Step 7.2

Simplify.

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Step 7.2.1

Multiply $12$ by $3$ .

$\frac{36 - 2 x \cdot 3 + y \cdot 3 + x + 4 y}{12}$

Step 7.2.2

Multiply $3$ by $- 2$ .

$\frac{36 - 6 x + y \cdot 3 + x + 4 y}{12}$

Step 7.2.3

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

$\frac{36 - 6 x + 3 \cdot y + x + 4 y}{12}$

Step 7.3

Add $- 6 x$ and $x$ .

$\frac{36 - 5 x + 3 y + 4 y}{12}$

Step 7.4

Add $3 y$ and $4 y$ .

$\frac{36 - 5 x + 7 y}{12}$