#### Answer

a. {$x$|$x$ is a real number, $x\ne-\frac{1}{7}$}
b. $(-∞,-\frac{1}{7})U(-\frac{1}{7},∞)$

#### Work Step by Step

We are given the function $f(x)=\frac{6x-5}{7x+1}$. The domain of the function will be all values of $x$ such that the denominator does not equal 0.
Therefore, we can set the denominator equal to 0. We will exclude from the domain all values of $x$ that make the denominator equal 0.
$7x+1=0$
Subtract 1 from both sides.
$7x=-1$
Divide both sides by 7.
$x=-\frac{1}{7}$
Therefore, the domain is {$x$|$x$ is a real number, $x\ne-\frac{1}{7}$} in set-builder notation and $(-∞,-\frac{1}{7})U(-\frac{1}{7},∞)$ in interval notation.