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

Nov 23, 2017

(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:

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

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: $\frac{x - 9}{x - 9} = 1$.

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

$\frac{6 b}{b - 4} \times \textcolor{t e a l}{\frac{b + 1}{b + 1}} - \frac{1}{b + 1} \times \textcolor{m a \ge n t a}{\frac{b - 4}{b - 4}}$

Simplify.

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

Combine.

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

Simplify.

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

Simplify.

$\frac{6 {b}^{2} + 5 b + 4}{\left(b + 1\right) \left(b - 4\right)}$