# Polynomial Division and Rational Expressions

### Topics

There are three steps to solving a math problem.

- Figure out what the problem is asking.

- Solve the problem.

- Check the answer.

Here's a fun story about camels that we've seen in several different puzzle books. A more literary version of the story can be found in *The Man Who Counted*.

### Sample Fun Camel Story

A man gave his three sons a herd of camels. He said that half of the camels should go to the eldest son, one-third of the camels should go to the middle son, and one-ninth of the camels should go to the youngest son.

Ugh, he probably divided them unfairly to start a fight. What a dromedary queen.

After dividing the camels, the sons found that there were two camels left over. How many camels were in the original herd? Also, is it true that the oldest brother titled his autobiography: "My Humps?"

1. Figure out what the problem is asking.

This part is fairly straightforward. Some camels got divided into groups, and we want to know how many total camels there are.

2. Solve the problem.

We'll translate the problem slowly from English into math. We know that

Since we know how many camels each son receives in terms of the total number of camels, it makes sense to have a variable for the total number of camels. We'll use c, for camel. Reading the problem again, we can translate each piece of the equation into symbols:

The overall equation translates into symbols as

.

From here, we know what to do. Isn't that the best feeling? We solve the equation using either of the two methods we learned earlier. Right now we'll do it by eliminating denominators, because that's what our Magic 8-Ball advised us to do. Start with the equation we found:

Multiply both sides by 18 (the LCD of 2, 3, and 9) to find

18

c= 9c+ 6c+ 2c+ 36,simplify to get

c= 36,and there we are.

3. Check the answer.

If there were originally 36 camels, then we should be able to give half of 36 to the eldest son, one-third of 36 to the middle son, one-ninth of 36 to the youngest son, and have 2 left over.

We do have 2 left over after the sons receive their camels.

On an entirely unrelated subject, if you're looking for camels to foster, please contact us here at Shmoop. We're determined to find them a good home. Warning: they spit.