Algebra Examples

$u (x) = - 2 x^{2} + 3$ $v (x) = \frac{1}{x}$

Step 1

Set up the composite result function.

$v (u (x))$

Step 2

Evaluate $v (- 2 x^{2} + 3)$ by substituting in the value of $u$ into $v$ .

$v (- 2 x^{2} + 3) = \frac{1}{- 2 x^{2} + 3}$

Step 3

Factor $- 1$ out of $- 2 x^{2}$ .

$v (- 2 x^{2} + 3) = \frac{1}{- (2 x^{2}) + 3}$

Step 4

Rewrite $3$ as $- 1 (- 3)$ .

$v (- 2 x^{2} + 3) = \frac{1}{- (2 x^{2}) - 1 \cdot - 3}$

Step 5

Factor $- 1$ out of $- (2 x^{2}) - 1 (- 3)$ .

$v (- 2 x^{2} + 3) = \frac{1}{- (2 x^{2} - 3)}$

Step 6

Rewrite negatives.

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Step 6.1

Rewrite $- (2 x^{2} - 3)$ as $- 1 (2 x^{2} - 3)$ .

$v (- 2 x^{2} + 3) = \frac{1}{- 1 (2 x^{2} - 3)}$

Step 6.2

Move the negative in front of the fraction.

$v (- 2 x^{2} + 3) = - \frac{1}{2 x^{2} - 3}$