Algebra Examples

$\frac{1}{x - 1} - \frac{7}{x^{2} + 5 x - 6}$

Step 1

Factor $x^{2} + 5 x - 6$ 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 $- 6$ and whose sum is $5$ .

$- 1, 6$

Step 1.2

Write the factored form using these integers.

$\frac{1}{x - 1} - \frac{7}{(x - 1) (x + 6)}$

Step 2

To write $\frac{1}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$\frac{1}{x - 1} \cdot \frac{x + 6}{x + 6} - \frac{7}{(x - 1) (x + 6)}$

Step 3

Multiply $\frac{1}{x - 1}$ by $\frac{x + 6}{x + 6}$ .

$\frac{x + 6}{(x - 1) (x + 6)} - \frac{7}{(x - 1) (x + 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{x + 6 - 7}{(x - 1) (x + 6)}$

Step 5

Subtract $7$ from $6$ .

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

Step 6

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{x + 6}$