Proofs: Problem 2


You aren't allowed to use fractions in your final proof. However, it may be helpful to write a proof using fractions and then set out to eliminate them. E.g. can you multiply everything in a sequence of equations by whatever's in the denominator?

Look at this example to see how to combine equations without using fractions.

Suppose I have a=b and c=d. Then I can multiply the first equation by c to get ac=bc. Multiply the second equation by b to get bc=bd. Now ac=bc=bd. So ac=bd.

For this kind of proof, it's not always clear what variable to choose when you multiply both sides by something. You may have to try several choices. Two things to watch, to guide what you're doing: