In the equation, $\frac15+\frac{5}{x}=\frac{12}{x}+\frac{1}{12}$, what is the value of $x$?
Right. Multiply both sides of the equation by $12x$. Now the equation is $12x*(\frac15+\frac{5}{x})=12x*(\frac{12}{x}+\frac{1}{12})$. Now we can subtract $x$ from both sides to get $\frac{12}{5} x + 60 - x = 144 + x - x$. So $\frac{12}{5} x + 60 - x = 144$. And we can subtract $60$ from both sides to get $\frac{12}{5} x + 60 - x - 60 = 144 - 60$. So $\frac{12}{5} x - x = 84$. And we can combine like terms to get $\frac{2}{5} x = 84$. What's the matter? Right. $12/5*x - x$ is $12/5*x - 5/5*x$ which is $7/5*x$. So $\frac{7}{5} x = 84$. And if we divide both sides by $7/5$ or multiply by $5/7$ we get $x=60$. Correct.

