Pre-Algebra Examples

$\frac{x (- 1) (x + 4) - 6 x}{x (x - 1)}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $x$ out of $x (- 1) (x + 4) - 6 x$ .

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Step 1.1.1

Factor $x$ out of $x (- 1) (x + 4)$ .

$\frac{x ((- 1) (x + 4)) - 6 x}{x (x - 1)}$

Step 1.1.2

Factor $x$ out of $- 6 x$ .

$\frac{x ((- 1) (x + 4)) + x \cdot - 6}{x (x - 1)}$

Step 1.1.3

Factor $x$ out of $x ((- 1) (x + 4)) + x \cdot - 6$ .

$\frac{x ((- 1) (x + 4) - 6)}{x (x - 1)}$

Step 1.2

Factor $- 1$ out of $- 1 (x + 4) - 6$ .

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Step 1.2.1

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{x (- 1 (x + 4) - 1 (6))}{x (x - 1)}$

Step 1.2.2

Factor $- 1$ out of $- 1 (x + 4) - 1 (6)$ .

$\frac{x (- 1 (x + 4 + 6))}{x (x - 1)}$

Step 1.2.3

Rewrite $- 1 (x + 4 + 6)$ as $- (x + 4 + 6)$ .

$\frac{x (- (x + 4 + 6))}{x (x - 1)}$

Step 1.3

Add $4$ and $6$ .

$\frac{x \cdot - 1 (x + 10)}{x (x - 1)}$

Step 1.4

Factor out negative.

$\frac{- x (x + 10)}{x (x - 1)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Cancel the common factor.

$\frac{- x (x + 10)}{x (x - 1)}$

Step 2.1.2

Rewrite the expression.

$\frac{- (x + 10)}{x - 1}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{x + 10}{x - 1}$