Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We start by factoring out all polynomials in the expression:

$\frac{b^2-2b-8}{b^2+b-2} -\frac{6}{b-1} =\\=\frac{(b-4)(b+2)}{(b+2)(b-1)}- \frac{6}{b-1}=$

where we can simplify the factor (b+2) that appears in numerator and denominator of the first rational expression, to reduce it to:

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

Now we can combine both rational expressions since they share the same denominator:

$\frac{b-4}{b-1} -\frac{6}{b-1} =\frac{b-4-6}{b-1} =\frac{b-10}{b-1}$