Miscellaneous Equations
If you look at the following equation, you would not say it is a quadratic
equation. However, by simplifying it, we obtain a quadratic equation and we
therefore apply methods for solving quadratic equations when trying to solving
it.
Example
An equation containing rational expressions
Solve
Solution
The least common denominator (LCD) for x, x  2, and 8 is 8x(x  2).


Multiply each side by the LCD. 



8x  16 + 24x 
= 5x^{2}  10x 

32x  16 
= 5x^{2}  10x 

5x^{2} + 42x  16 
= 0 

5x^{2}  42x + 16 
= 0 
Multiply each side by 1 for easier factoring. 
(5x  2)(x  8) 
= 0 
Factor. 
5x  2 
= 0 
or 
x  8 
= 0 

x 

or 
x 
= 8 

Check these values in the original equation. The solution set is
.
