Simplify (b^2-2b-8)/(b^2+b-2)-6/(b-1)

$\frac{b^{2} - 2 b - 8}{b^{2} + b - 2} - \frac{6}{b - 1}$

Step 1

Simplify each term.

Factor $b^{2} - 2 b - 8$ using the AC method.

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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Write the factored form using these integers.

$\frac{(b - 4) (b + 2)}{b^{2} + b - 2} - \frac{6}{b - 1}$

Factor $b^{2} + b - 2$ using the AC method.

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 $- 2$ and whose sum is $1$ .

$- 1, 2$

Write the factored form using these integers.

$\frac{(b - 4) (b + 2)}{(b - 1) (b + 2)} - \frac{6}{b - 1}$

Cancel the common factor of $b + 2$ .

Cancel the common factor.

$\frac{(b - 4) (b + 2)}{(b - 1) (b + 2)} - \frac{6}{b - 1}$

Rewrite the expression.

$\frac{b - 4}{b - 1} - \frac{6}{b - 1}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{b - 4 - 6}{b - 1}$

Subtract $6$ from $- 4$ .

$\frac{b - 10}{b - 1}$

Simplify (b^2-2b-8)/(b^2+b-2)-6/(b-1)

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