## Precalculus: Mathematics for Calculus, 7th Edition

$x=-\dfrac{1}{3}$
$\dfrac{1}{x}=\dfrac{4}{3x}+1$ Let's multiply the whole equation by $3x$, which is the least common multiple of the denominators present in the equation. We'll do this to avoid working with fractions. $(3x)(\dfrac{1}{x}=\dfrac{4}{3x}+1)$ $(3x)(\dfrac{1}{x})=(3x)(\dfrac{4}{3x})+3x$ Simplify: $3=4+3x$ Solve for $x$: $3x=3-4$ $3x=-1$ $x=-\dfrac{1}{3}$