Math Snap

STEP 1

Assumptions1. The given rational expression is $\frac{5 c^{}-15 c^{3}}{20 c^{} d+25 c^{}}$

STEP 2

First, we need to factor out the common factors from the numerator and the denominator. In the numerator, we can factor out $5c^2$. In the denominator, we can factor out $5c^2$.
$$\frac{5 c^{2}-15 c^{}}{20 c^{2} d+25 c^{2}} = \frac{5c^2(1-c)}{5c^2(4d+5)}$$

After factoring, we can cancel out the common factors from the numerator and the denominator. In this case, $5c^2$ is a common factor that can be cancelled out.
$$\frac{5c^2(1-3c)}{5c^2(d+5)} = \frac{1-3c}{d+5}$$The equivalent expression is $\frac{1-3c}{d+5}$.