College Algebra & Trigonometry, 2018a

1.9. RATIONAL EQUATIONS 73
Sometimes, it is helpful to create a common denominator in order to set up a
situation where cross-multiplying can be used.
Example
Solve for x.
1
x +6 + 4
x − 2 = 3
x +1
1
x +6 + 4
x − 2 = 3
x +1
1
x +6 ∗ x − 2
x − 2 + 4
x − 2 ∗ x +6
x +6 = 3
x +1
1(x − 2) + 4(x +6)
(x +6)(x − 2)
= 3
x +1
x − 2+4x +24
(x +6)(x − 2) = 3
x +1
5x +22
(x +6)(x − 2) = 3
x +1
(5x + 22)(x +1)=3(x +6)(x − 2) = 3(x 2 +4x − 12)
5x 2 +27x +22=3x 2 +12x − 36
2x 2 +15x +58=0
x ≈−3.75 ± 3.865i