Finite Math Examples

$\frac{4 - x}{x^{2} + 3 x - 28}$

Step 1

Factor $x^{2} + 3 x - 28$ using the AC method.

Tap for more steps...

Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 28$ and whose sum is $3$ .

$- 4, 7$

Step 1.2

Write the factored form using these integers.

$\frac{4 - x}{(x - 4) (x + 7)}$

Step 2

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1

Cancel the common factor of $4 - x$ and $x - 4$ .

Tap for more steps...

Step 2.1.1

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- 1 (- 4) - x}{(x - 4) (x + 7)}$

Step 2.1.2

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

$\frac{- 1 (- 4) - (x)}{(x - 4) (x + 7)}$

Step 2.1.3

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

$\frac{- 1 (- 4 + x)}{(x - 4) (x + 7)}$

Step 2.1.4

Reorder terms.

$\frac{- 1 (x - 4)}{(x - 4) (x + 7)}$

Step 2.1.5

Cancel the common factor.

$\frac{- 1 (x - 4)}{(x - 4) (x + 7)}$

Step 2.1.6

Rewrite the expression.

$\frac{- 1}{x + 7}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{x + 7}$