Answer
See answers below
Work Step by Step
$a) \frac{1}{3}+\frac{3}{x}=\frac{2}{x}$
$3x(\frac{1}{3}+\frac{3}{x})=3x(\frac{2}{x})$
$x+9=6$
$x=-3$
Check: $\frac{1}{3}+\frac{3}{-3}=\frac{2}{-3}$
$\frac{-2}{3}=\frac{-2}{3}$
$b) \frac{4}{7x}+\frac{1}{3}=\frac{7}{3x}$
$21x( \frac{4}{7x}+\frac{1}{3})=21x(\frac{7}{3x})$
$12+7x=49$
$x=\frac{37}{7}$
Check: $ \frac{4}{7(\frac{37}{7})}+\frac{1}{3}=\frac{7}{3(\frac{37}{7})}$
$\frac{49}{111}=\frac{49}{111}$
