1	Equations with Algebraic Fractions
2	To Factor Algebraic Fractions a. Factor the denominators b. Find the least common denominator (LCD) c. Multiply each side of the equation by the LCD d. Solve for the variable e. Check for a valid solution by substituting the result into the original problem. A solution is invalid if the denominator becomes zero. A solution is invalid if the two sides of the equation are not equal.
3	Algebraic Fractions Example 1 a. Factor the denominators 9 = 3 ·3 7 = 7 ·1 b. LCD = 3 ·3 ·7 = 63 c. Multiply each side of the equation by the LCD
4	Example 1 page 2 d. Solve for the variable e. Check the solution in the original equation 7x + 9x = 63 16x = 63
5	Algebraic Fractions Example 2 a. Factor the denominators 3 = 3 ·1, 4 = 2 ·2, 2 = 2 · 1 b. LCD = 3 ·2 ·2 = 12 c. Multiply each side of the equation by the LCD
6	Example 2 page 2 d. Solve for the variable e. Check the solution in the original equation
7	Algebraic Fractions Example 3 a. Factor the denominators 4 = 2 ·2 y + 2 (not factorable) 28 = 2 ·2 ·7 b. LCD = 2 ·2 ·7·(y + 2) = 28 (y + 2) c. Multiply each side of the equation by the LCD
8	Example 3 page 2 d. Solve for the variable e. Check the solution in the original equation
9	Algebraic Fractions Example 4 a. Factor the denominators 5 (not factorable) 2p-1 (not factorable) b. LCD = 5(2p-1) c. Multiply each side of the equation by the LCD
10	Example 4 page 2
11	Example 4 page 3 e. Check the solutions in the original equation for for
12	Algebraic Fractions Example 5 a. Factor the denominators r + 2 (not factorable) r - 5 (not factorable) b. LCD = (r + 2)(r - 5) c. Multiply each side of the equation by the LCD
13	Example 5 page 2 d. Solve for the variable e. Check the solution in the original equation Note: This is the exact form of the original equation that would be obtained by cross multiplying
14	Algebraic Fractions Example 6
15	Example 6 page 2 d. Solve for the variable e. Check the solutions in the original equation for r = 3 for r = -1 The denominator becomes zero. -1 can not be a solution.