How do you simplify b/(b+3)+6/(b-2)?

Apr 13, 2017

$\frac{{b}^{2} + 4 b + 18}{\left(b + 3\right) \left(b - 2\right)}$

Explanation:

Finding the LCD involves application of LCM;

LCM of $\left(b + 3\right) \mathmr{and} \left(b - 2\right) = \left(b + 3\right) \left(b - 2\right)$

Multiply each fraction as necessary to create equivalent fractions.

$\frac{b}{b + 3} \times \frac{b - 2}{b - 2} + \frac{6}{b - 2} \times \frac{b + 3}{b + 3}$

Now simplify each fraction:

$\frac{b \left(b - 2\right)}{\left(b + 3\right) \left(b - 2\right)} + \frac{6 \left(b + 3\right)}{\left(b + 3\right) \left(b - 2\right)}$

Now combine into one fraction:

$= \frac{{b}^{2} - 2 b + 6 b + 18}{\left(b + 3\right) \left(b - 2\right)}$

$= \frac{{b}^{2} + 4 b + 18}{\left(b + 3\right) \left(b - 2\right)}$