Answer
True
Work Step by Step
We are given the division:
$$\dfrac{f(x)}{g(x)}\div\dfrac{h(x)}{k(x)}.$$
We have to add three restrictions in order to have this division make sense:
- the denominator of the first fraction must not be zero so that the fraction $\dfrac{f(x)}{g(x)}$ is defined: $g(x)\not=0$;
- the denominator of the second fraction must not be zero so that the fraction $\dfrac{h(x)}{k(x)}$ is defined: $k(x)\not=0$;
- the numerator of the second fraction must not be zero so that when we change division to multiplication by $\dfrac{k(x)}{h(x)}$ the fraction $\dfrac{k(x)}{h(x)}$ is defined: $h(x)\not=0$.
So the three conditions are:
$$\begin{cases}
g(x)\not=0\\
k(x)\not=0\\
h(x)\not=0.
\end{cases}$$
The given statement is TRUE.
