9 Rational expressions
To simplify rational expressions, expand the powers and then cancel.
For example, . In this example, we cancelled a 2 times, in both the numerator and denominator.
Another example, . In this example, the denominator is 1, but dividing anything by 1 just gives itself.
If we had , note we now have a plus sign (rather than just multiply). To solve this, we could factor out the from the numerator (top) and then cancel. This would give us , and cancelling out the , we have .
Alternatively, we can split the quotient into 2 parts before cancelling. That is, .
I find the 2nd method easier.