Question

How do you combine `(6b)/(b-4)-1/(b+1)`?

Answer 1

`(6b(b+1))/((b+1)(b-4))-(b-4)/((b+1)(b-4))=color(blue)((6b^2+5b+4)/((b+1)(b-4))`
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Explanation:

Combine:

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

In order to add or subtract fractions, they must have the same denominator. For denominators that are binomials, we can multiply both binomials by a form of `1` that will give them the same denominator. For example: `(x-9)/(x-9)=1`.

Multiply both binomials so that they will have the same denominator, `(b+1)(b-4)`.

`(6b)/(b-4)xxcolor(teal)((b+1)/(b+1))-(1)/(b+1)xxcolor(magenta)((b-4)/(b-4))`

Simplify.

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

Combine.

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

Simplify.

`(6b^2+6b-b+4)/((b+1)(b-4))`

Simplify.

`(6b^2+5b+4)/((b+1)(b-4))`