Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

$\frac{x - 4 y - (4 x + 5 y)}{12 x}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{x - 4 y - (4 x) - (5 y)}{12 x}$

Step 2.2

Multiply $4$ by $- 1$ .

$\frac{x - 4 y - 4 x - (5 y)}{12 x}$

Step 2.3

Multiply $5$ by $- 1$ .

$\frac{x - 4 y - 4 x - 5 y}{12 x}$

$\frac{x - 4 y - 4 x - 5 y}{12 x}$

Step 3

Simplify terms.

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Step 3.1

Subtract $4 x$ from $x$ .

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

Step 3.2

Subtract $5 y$ from $- 4 y$ .

$\frac{- 3 x - 9 y}{12 x}$

Step 3.3

Cancel the common factor of $- 3 x - 9 y$ and $12$ .

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Step 3.3.1

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 9 y}{12 x}$

Step 3.3.2

Factor $3$ out of $- 9 y$ .

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

Step 3.3.3

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

$\frac{3 (- x - 3 y)}{12 x}$

Step 3.3.4

Cancel the common factors.

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Step 3.3.4.1

Factor $3$ out of $12 x$ .

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

Step 3.3.4.2

Cancel the common factor.

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

Step 3.3.4.3

Rewrite the expression.

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

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

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

Step 3.4

Factor $- 1$ out of $- x$ .

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

Step 3.5

Factor $- 1$ out of $- 3 y$ .

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

Step 3.6

Factor $- 1$ out of $- (x) - (3 y)$ .

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

Step 3.7

Simplify the expression.

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Step 3.7.1

Rewrite $- (x + 3 y)$ as $- 1 (x + 3 y)$ .

$\frac{- 1 (x + 3 y)}{4 x}$

Step 3.7.2

Move the negative in front of the fraction.

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$