Trigonometry Examples

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

Step 1

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

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Step 1.1

Factor $- 1$ out of $x$ .

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

Step 1.2

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 1.3

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

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

Step 1.4

Reorder terms.

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

Step 1.5

Cancel the common factor.

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

Step 1.6

Rewrite the expression.

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

Step 2

Cancel the common factor of $x + 2$ and $2 + x$ .

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Step 2.1

Reorder terms.

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Factor out negative.

$\frac{- (x + 5) (3 - x)}{(5 - x) (3 + x)}$

Step 4

Move the negative in front of the fraction.

$- \frac{(x + 5) (3 - x)}{(5 - x) (3 + x)}$