6.4 Part III - Solve Rational Equations

We need a common denominator, right?

 $\frac{1}{2}+\frac{1}{3}=?$  

What is the LCM of 2 & 3? Six, right? So our common denominator is 6.

So we multiply the top and bottom of both fractions by the "missing factor". $\frac{1\cdot3}{2\cdot3}+\frac{1\cdot2}{3\cdot2}=\frac{3+2}{6}=\frac{5}{6}$  

 $\frac{6}{x}+\frac{5}{4}=-\frac{7}{4}$  

We have an x and a 4 for denominators, so our LCM is 4*x = 4x

 $\frac{6\cdot4}{x\cdot4}+\frac{5\cdot x}{4\cdot x}=-\frac{7\cdot x}{4\cdot x}$  

 $\frac{24}{4x}+\frac{5x}{4x}=-\frac{7x}{4x}$  

 $24+5x=-7x$  

 $24=-12x$  

 $-2=x$