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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				= 5x² - 10x
32x - 16				= 5x² - 10x
-5x² + 42x - 16				= 0
5x² - 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 .