College Algebra & Trigonometry, 2018a

72 CHAPTER 1. ALGEBRA REVIEW
If a problem is stated simply as the equality of two fractions, cross-multiplying
can be a useful method of solution.
Example
Solve for x.
x
2x +3 = 7
x − 4
x
2x +3 = 7
x − 4
x(x − 4) = 7(2x +3)
x 2 − 4x =14x +21
x 2 − 18x − 21 = 0
x ≈ 19.100, −1.100
Cross-multiplying is really just a short-cut method of clearing out the denominators
by multiplying on both sides by both denominators:
(x − 4)(2x +3)∗
x
2x +3 = 7
x − 4
x
2x +3 = 7 ∗ (x − 4)(2x +3)
x − 4
x
(x − 4) ✘ (2x ✘✘✘✘
+3)∗
✘✘✘✘
2x +3 = 7
✘✘✘ x − 4 ∗ ✘✘✘✘
(x − 4)(2x +3)
x(x − 4) = 7(2x +3)
Then the equation is ready to be solved as shown above - but by just crossmulitiplying,
we skip directly to the solution portion of the problem.