Answer
$\frac{g}{f}(x) = g(x) \div f(x) = \dfrac{x^2}{7x + 5}$
$\text{Domain: all real numbers except } -\frac{5}{7}$
Work Step by Step
This exercise asks us to divide one function by another. Let's write out the problem:
$\frac{g}{f}(x) = g(x) \div f(x) = \dfrac{x^2}{7x + 5}$
We cannot simplify this expression any further.
When we find the domain, we want to find which values of $x$ will cause the function to become undefined; in other words, we want to find any restrictions for $x$ so we can exclude them from the domain.
To find the restrictions for $x$, we set the denominator equal to $0$ and solve for $x$:
$7x + 5 = 0$
$7x = -5$
Divide each side by $7$:
$x = -\frac{5}{7}$
In this exercise, $x$ can be any real number except for $-\frac{5}{7}$.
