This week in PreCalc 11 we learned about rational expressions. Rational Expressions are fractions whose numerator and denominator are both polynomials. They are usually given in unfactored form, and the point is to simplify them, just like a regular fraction, and determine which numbers x cannot equal.

Example:

Explanation:

Step 1: Factor Numerator

In this example, the factoring is simple. All that needs to be done is find two numbers that add to 11 and the product of those two numbers equal 30.

Step 2: Factor Denominator

In this example, the denominator is a difference of squares so to factor is two figure out the conjugates of the square roots of both terms of the polynomial.

Step 3: find what x can’t equal

For fractions, in general, the denominator can never equal zero. Same rule applies for rational expressions, the denominator cannot equal zero. In this example, if x was 5 or -5 then the denominator will equal zero which can never happen. So because of that, we must write that x cannot equal 5 or -5.

Step 4: simplify

Once the fraction is completely factored then cross out factors that are the same on the top and the bottom. In this example, (x +5) is on the top and the bottom so we can cross those out. We can only cross out complete factors that are the same, not single terms. For example, if there was a 3 on the top and 3 on the bottom then we couldn’t cross those out. We could cross them out if it was (x + 3).

Step 5: final answer

After simplifying the fraction, then that leaves you with the final answer.