Algebra Examples

$\frac{x + 2}{10 y} + \frac{3 x - 1}{10 y} - \frac{2 x + 5}{10 y}$

Step 1

Combine the numerators over the common denominator.

$\frac{x + 2 + 3 x - 1 - (2 x + 5)}{10 y}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{x + 2 + 3 x - 1 - (2 x) - 1 \cdot 5}{10 y}$

Step 2.2

Multiply $2$ by $- 1$ .

$\frac{x + 2 + 3 x - 1 - 2 x - 1 \cdot 5}{10 y}$

Step 2.3

Multiply $- 1$ by $5$ .

$\frac{x + 2 + 3 x - 1 - 2 x - 5}{10 y}$

Step 3

Simplify terms.

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Step 3.1

Add $x$ and $3 x$ .

$\frac{4 x + 2 - 1 - 2 x - 5}{10 y}$

Step 3.2

Subtract $2 x$ from $4 x$ .

$\frac{2 x + 2 - 1 - 5}{10 y}$

Step 3.3

Simplify by subtracting numbers.

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Step 3.3.1

Subtract $1$ from $2$ .

$\frac{2 x + 1 - 5}{10 y}$

Step 3.3.2

Subtract $5$ from $1$ .

$\frac{2 x - 4}{10 y}$

Step 3.4

Cancel the common factor of $2 x - 4$ and $10$ .

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Step 3.4.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 4}{10 y}$

Step 3.4.2

Factor $2$ out of $- 4$ .

$\frac{2 x + 2 \cdot - 2}{10 y}$

Step 3.4.3

Factor $2$ out of $2 x + 2 \cdot - 2$ .

$\frac{2 (x - 2)}{10 y}$

Step 3.4.4

Cancel the common factors.

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Step 3.4.4.1

Factor $2$ out of $10 y$ .

$\frac{2 (x - 2)}{2 (5 y)}$

Step 3.4.4.2

Cancel the common factor.

$\frac{2 (x - 2)}{2 (5 y)}$

Step 3.4.4.3

Rewrite the expression.

$\frac{x - 2}{5 y}$