2. Example 5A: Solving Simple Rational Equations
Solve. Check your solution.
x2 – 25
x – 5
= 14
(x + 5)(x – 5)
(x – 5)
= 14
Note that x ≠ 5.
x + 5 = 14
x = 9

3. Example 5A Continued
x2 – 25
x – 5
= 14
Check
(9)2 – 25
9 – 5 14 56 4 14

4. Example 5B: Solving Simple Rational Equations
Solve. Check your solution.
x2 + 3x - 10
x – 2
= 7
(x + 5)(x – 2)
(x – 2)
= 7
Note that x ≠ 2.
x + 5 = 7
x = 2
Because the left side of the original equation is undefined when x = 2, there is no solution.

5. Example 5B Continued
Check A graphing calculator shows that 2 is not a solution.

6. Check It Out! Example 5a
Solve. Check your solution.
x2 + x – 12
x + 4
= –7
(x – 3)(x + 4)
(x + 4)
= –7
Note that x ≠ –4.
x – 3 = –7
x = –4
Because the left side of the original equation is undefined when x = –4, there is no solution.

7. Check It Out! Example 5a Continued
Check A graphing calculator shows that –4 is not a solution.

8. Check It Out! Example 5b
Solve. Check your solution.
4x2 – 9
2x + 3
= 5
(2x + 3)(2x – 3)
(2x + 3)
= 5
Note that x ≠ – 3 2
2x – 3 = 5
x = 4

9. Check It Out! Example 5b Continued
= 5
Check
4(4)2 – 9
2(4) + 3 5 55 11 5