Simplify $\frac{x}{c} - \frac{x}{c-d}$ There's a long time that I don't solve questions like this one. I'm having problems to simplify this one:

$$\frac{x}{c} - \frac{x}{c-d}$$
First recall that
\[
\frac{a}{b}-\frac{c}{d}= \frac{ad-bc}{bd}
\]
Then
\[
\frac{x}{c}-\frac{x}{c-d}= x\left(\frac{1}{c}-\frac{1}{c-d}\right)= x\left(\frac{c-d-c}{c(c-d)}\right)= \frac{-xd}{c^2-cd}
\]
I attempted to be as clear as possible.
Multiply the first term by $\frac{c-d}{c-d}$ and the second term by $\frac{c}{c}$ Then you will have $\frac{x(c-d)-x(c)}{c(c-d)} = \frac{-xd}{c(c-d)}$