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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) = (x2 + 20x)10 Simplify.
200x + 4000 + 300x = 10x2 + 200x  
4000 + 300x = 10x2 Combine like terms.
400 + 30x = x2 Divide each side by 10.
0 = x2 - 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}.

 

 
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