Precalculus Examples

$2 x {(x - 5)}^{- 3} - 4 x^{2} {(x - 5)}^{- 4}$

Step 1

Factor $2 x {(x - 5)}^{- 4}$ out of $2 x {(x - 5)}^{- 3} - 4 x^{2} {(x - 5)}^{- 4}$ .

Tap for more steps...

Step 1.1

Factor $2 x {(x - 5)}^{- 4}$ out of $2 x {(x - 5)}^{- 3}$ .

$2 x {(x - 5)}^{- 4} (x - 5) - 4 x^{2} {(x - 5)}^{- 4}$

Step 1.2

Factor $2 x {(x - 5)}^{- 4}$ out of $- 4 x^{2} {(x - 5)}^{- 4}$ .

$2 x {(x - 5)}^{- 4} (x - 5) + 2 x {(x - 5)}^{- 4} (- 2 x)$

Step 1.3

Factor $2 x {(x - 5)}^{- 4}$ out of $2 x {(x - 5)}^{- 4} (x - 5) + 2 x {(x - 5)}^{- 4} (- 2 x)$ .

$2 x {(x - 5)}^{- 4} (x - 5 - 2 x)$

Step 2

Subtract $2 x$ from $x$ .

$2 x {(x - 5)}^{- 4} (- x - 5)$

Step 3

Factor.

Tap for more steps...

Step 3.1

Factor $- 1$ out of $- x - 5$ .

Tap for more steps...

Step 3.1.1

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

$2 x {(x - 5)}^{- 4} (- (x) - 5)$

Step 3.1.2

Rewrite $- 5$ as $- 1 (5)$ .

$2 x {(x - 5)}^{- 4} (- (x) - 1 (5))$

Step 3.1.3

Factor $- 1$ out of $- (x) - 1 (5)$ .

$2 x {(x - 5)}^{- 4} (- (x + 5))$

Step 3.2

Remove unnecessary parentheses.

$2 x {(x - 5)}^{- 4} \cdot - 1 (x + 5)$

Step 4

Combine exponents.

Tap for more steps...

Step 4.1

Factor out negative.

$- (2 x {(x - 5)}^{- 4} (x + 5))$

Step 4.2

Multiply $2$ by $- 1$ .

$- 2 (x {(x - 5)}^{- 4} (x + 5))$

Step 5

Remove unnecessary parentheses.

$- 2 x {(x - 5)}^{- 4} (x + 5)$