Question

In the following expression, perform the indicated operation:

$\frac{5a}{a-2}+\frac{9}{a}-\frac{2a+18}{a^2-2a}$

Short answer

$\frac{5a^2+7a-36}{a\left(a-2\right)}$

Step-by-step solution

Step 1. Given information.

The following expression is given:

$\frac{5a}{a-2}+\frac{9}{a}-\frac{2a+18}{a^2-2a}$

Step 2. Perform the indicated operation.

Factor the denominator and numerator (where applicable):

$\frac{5a}{a-2}+\frac{9}{a}-\frac{2\left(a+9\right)}{a\left(a-2\right)}$

Find the LCD:

$a\left(a-2\right)$

Rewrite the expression with LCD at the denominator:

role="math" localid="1644731961868" $\frac{5a^2}{a\left(a-2\right)}+\frac{9\left(a-2\right)}{a\left(a-2\right)}-\frac{2a+18}{a\left(a-2\right)}$

Simplify:

role="math" localid="1644732100403" $$\begin{gathered} \frac{5a^2+9a-18-2a-18}{a\left(a-2\right)} \\ \frac{5a^2+7a-36}{a\left(a-2\right)} \end{gathered}$$