Solving Equations Involving Rational Expressions
To solve an equation with rational expressions, we do not convert
the rational expressions to ones with a common denominator. Instead, we
multiply each side by the LCD to eliminate the denominators.
Example 1
An equation with two solutions
Solve
Solution

= x(x + 20)10 
Multiply each side by
x(x + 20). 

= x(x + 20)10 
Distributive property 
(x + 20)200 + x(300) 
= (x^{2} + 20x)10 
Simplify. 
200x + 4000 + 300x 
= 10x^{2} + 200x 

4000 + 300x 
= 10x^{2} 
Combine like terms. 
400 + 30x 
= x^{2} 
Divide each side by 10. 
0 
= x^{2}  30x  400 

0 
= (x  40)(x + 10) 
Factor. 
x  40 = 0 
or 
x + 10 
= 0 
Set each factor equal
to 0. 
x = 40 
or 
x 
= 10 

Check these values in the original equation. The solution set is {10, 40}.
