Solving a Rational Equation

Solve the rational equation: $\frac{7}{2 x} - \frac{5}{3 x} = \frac{22}{3} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We have three denominators; $2 x, 3 x,$ and 3. The LCD must contain $2 x, 3 x,$ and 3. An LCD of $6 x$ contains all three denominators. In other words, each denominator can be divided evenly into the LCD. Next, multiply both sides of the equation by the LCD $6 x .$

$\begin{matrix} (6 x) (\frac{7}{2 x} - \frac{5}{3 x}) & = & (\frac{22}{3}) (6 x) \\ (6 x) (\frac{7}{2 x}) - (6 x) (\frac{5}{3 x}) & = & (\frac{22}{3}) (6 x) & Use the distributive property . \\ (6 x) (\frac{7}{2 x}) - (6 x) (\frac{5}{3 x}) & = & (\frac{22}{3}) (6 x) & Cancel out the common factors . \\ 3 (7) - 2 (5) & = & 22 (2 x) & Multiply remaining factors by each numerator . \\ 21 - 10 & = & 44 x \\ 11 & = & 44 x \\ \frac{11}{44} & = & x \\ \frac{1}{4} & = & x \end{matrix}$

How did it go?