1. Equations with Algebraic Fractions
Kathy Lyden's 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.
Kathy Lyden's Equations with Algebraic Fractions

3. Kathy Lyden's Equations with Algebraic Fractions
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
Kathy Lyden's Equations with Algebraic Fractions

4. Kathy Lyden's Equations with Algebraic Fractions
Example page 2
d. Solve for the variable e. Check the solution in
the original equation
7x + 9x = 63
16x = 63
Kathy Lyden's Equations with Algebraic Fractions

5. Kathy Lyden's Equations with Algebraic Fractions
Algebraic Fractions Example 2
a. Factor the denominators
3 = 3 ·1, = 2 ·2, = 2 · 1
b. LCD = 3 ·2 ·2 = 12
c. Multiply each side of the equation by the LCD
Kathy Lyden's Equations with Algebraic Fractions

6. Kathy Lyden's Equations with Algebraic Fractions
Example page 2
d. Solve for the variable e. Check the solution in the original equation
Kathy Lyden's Equations with Algebraic Fractions

7. Kathy Lyden's Equations with Algebraic Fractions
Algebraic Fractions Example 3
a. Factor the denominators
4 = 2 ·2
y (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
Kathy Lyden's Equations with Algebraic Fractions

8. Kathy Lyden's Equations with Algebraic Fractions
Example page 2
d. Solve for the variable e. Check the solution in the original equation 7 | | | | | |
Kathy Lyden's Equations with Algebraic Fractions

9. Kathy Lyden's Equations with Algebraic Fractions
Algebraic Fractions Example 4
a. Factor the denominators
(not factorable)
2p-1 (not factorable)
b. LCD = 5(2p-1)
c. Multiply each side of the equation by the LCD
Kathy Lyden's Equations with Algebraic Fractions

10. Kathy Lyden's Equations with Algebraic Fractions
Example page 2
d. Solve for the variable
and | | | |
Kathy Lyden's Equations with Algebraic Fractions

11. Kathy Lyden's Equations with Algebraic Fractions
Example page 3
e. Check the solutions in the original equation
for for
+ 1 .
- 1 + -
Kathy Lyden's Equations with Algebraic Fractions

12. Algebraic Fractions Example 5
a. Factor the denominators
r + 2 (not factorable)
r (not factorable)
b. LCD = (r + 2)(r - 5)
c. Multiply each side of the equation by the LCD
Kathy Lyden's Equations with Algebraic Fractions

13. Kathy Lyden's Equations with Algebraic Fractions
Example 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 | | | |
Kathy Lyden's Equations with Algebraic Fractions

14. Kathy Lyden's Equations with Algebraic Fractions
Algebraic Fractions Example 6
a. Factor the denominators
r2 - 1 = (r + 1)(r - 1)
r (not factorable)
b. LCD = (r + 1)(r - 1)
c. Multiply each side of the equation by the LCD
Kathy Lyden's Equations with Algebraic Fractions

15. Kathy Lyden's Equations with Algebraic Fractions
Example 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. | | | | | / /
and
Kathy Lyden's Equations with Algebraic Fractions