5.If = , what is the value of ?A)
B)
C) 2
D) 3
Here’s How to Crack It
This question appears in the No Calculator section, so you must use your math skills to solve for r. You
can cross multiply to get 18r = 3(r + 10) or 18r = 3r + 30. Subtracting 3r from both sides gives you 15r =
30, so r = 2. Finally, = , which is (A).
Extraneous Solutions
Sometimes solving a rational or radical expression makes funny things happen. Let’s look at an example.
Given the equation above, what is the value of z ?
Here’s How to Crack It
Use the Bowtie method to get a common denominator for the fractions on the left side of the equation. The
numerator of the fraction on the left becomes (z – 2) and the numerator of the fraction on the right becomes
(z + 2). The numerators are added together, and the new denominator is the product of the old ones. The
equation becomes
Since the denominators are equal, the numerators are equal. This gives you
(z – 2) + (z + 2) = 4When you simplify the left side, you get 2z = 4, so z = 2. Sounds great, right? However, you need to plug
this solution back into the original equation to make sure that it works. You get