Algebra Examples

$\frac{2 x + 3 y}{9 x} + \frac{6 x - 11 y}{9 x} - \frac{19 y - x}{9 x}$

Step 1

Combine the numerators over the common denominator.

$\frac{2 x + 3 y + 6 x - 11 y - (19 y - x)}{9 x}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{2 x + 3 y + 6 x - 11 y - (19 y) - - x}{9 x}$

Step 2.2

Multiply $19$ by $- 1$ .

$\frac{2 x + 3 y + 6 x - 11 y - 19 y - - x}{9 x}$

Step 2.3

Multiply $- - x$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$\frac{2 x + 3 y + 6 x - 11 y - 19 y + 1 x}{9 x}$

Step 2.3.2

Multiply $x$ by $1$ .

$\frac{2 x + 3 y + 6 x - 11 y - 19 y + x}{9 x}$

Step 3

Simplify terms.

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Step 3.1

Add $2 x$ and $6 x$ .

$\frac{8 x + 3 y - 11 y - 19 y + x}{9 x}$

Step 3.2

Add $8 x$ and $x$ .

$\frac{9 x + 3 y - 11 y - 19 y}{9 x}$

Step 3.3

Subtract $11 y$ from $3 y$ .

$\frac{9 x - 8 y - 19 y}{9 x}$

Step 3.4

Subtract $19 y$ from $- 8 y$ .

$\frac{9 x - 27 y}{9 x}$

Step 3.5

Cancel the common factor of $9 x - 27 y$ and $9$ .

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Step 3.5.1

Factor $9$ out of $9 x$ .

$\frac{9 (x) - 27 y}{9 x}$

Step 3.5.2

Factor $9$ out of $- 27 y$ .

$\frac{9 (x) + 9 (- 3 y)}{9 x}$

Step 3.5.3

Factor $9$ out of $9 (x) + 9 (- 3 y)$ .

$\frac{9 (x - 3 y)}{9 x}$

Step 3.5.4

Cancel the common factors.

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Step 3.5.4.1

Factor $9$ out of $9 x$ .

$\frac{9 (x - 3 y)}{9 (x)}$

Step 3.5.4.2

Cancel the common factor.

$\frac{9 (x - 3 y)}{9 x}$

Step 3.5.4.3

Rewrite the expression.

$\frac{x - 3 y}{x}$