Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

Combine $x$ and $\frac{2}{2}$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $- - y$ .

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Step 3.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.3.2

Multiply $y$ by $1$ .

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

Step 3.4

Subtract $x$ from $2 x$ .

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

Step 4

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

$\frac{x + y}{2} \cdot \frac{2}{2} + \frac{x + y}{4}$

Step 5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{x + y}{2}$ by $\frac{2}{2}$ .

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

Step 5.2

Multiply $2$ by $2$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{x \cdot 2 + y \cdot 2 + x + y}{4}$

Step 7.2

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

$\frac{2 \cdot x + y \cdot 2 + x + y}{4}$

Step 7.3

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

$\frac{2 \cdot x + 2 \cdot y + x + y}{4}$

Step 7.4

Multiply $2$ by $y$ .

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

Step 7.5

Add $2 x$ and $x$ .

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

Step 7.6

Add $2 y$ and $y$ .

$\frac{3 x + 3 y}{4}$

Step 7.7

Factor $3$ out of $3 x + 3 y$ .

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Step 7.7.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 3 y}{4}$

Step 7.7.2

Factor $3$ out of $3 y$ .

$\frac{3 (x) + 3 (y)}{4}$

Step 7.7.3

Factor $3$ out of $3 (x) + 3 (y)$ .

$\frac{3 (x + y)}{4}$