Question

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

Answer 1

`(b-10)/(b-1)`

Explanation:

We start by factoring out all polynomials in the expression:

`(b^2-2b-8)/(b^2+b-2) -(6)/(b-1) =\\=((b-4)(b+2))/((b+2)(b-1))- (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:

`(b-4)/(b-1) -(6)/(b-1)`

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

`(b-4)/(b-1) -(6)/(b-1) =(b-4-6)/(b-1) =(b-10)/(b-1)`