This week in PreCalc 11 we learned how to solve rational equations. Rational equations are equations containing at least one fraction whose numerator or denominator is a variable.

There are two ways to solve rational equations, one of them is multiplying every term by each of the denominators or cross multiplication. Cross multiplication only works when there are two fractions and one is on each side of the equal sign whereas multiplying by the denominator is a strategy that will work with every type of rational equation.

Example:

Explanation:

Step 1: Factor

Factor any polynomials that aren’t already factored. To factor, find two numbers that when multiplied together equal the last term and when added together equal the middle term.

Step 2: Multiply by the Denominator

Multiplying by the denominator is just doing the opposite operation to take the fraction away to make the equation easier to solve. When you have a fraction it means that its the numerator divided by the denominator, so to get rid of the denominator, we should multiply the term by the denominator to get rid of it. If we multiply the term by it, then the same term that is on the denominator will also be apart of the numerator making them cancel out. But what we do to one term, we do to every term, so we have to multiply each term in the equation by the denominator. Typically there is more than one denominator, so we follow the same procedure for the rest of the fractions.

Step 3: Non-Permissible Values

Non permissible values are numbers in which x cannot equal because it will make the denominators zero which can never happen. So stating non permissible values is important. In this case, the denominators consists of (b – 2), (b +2), and (b – 3) so b cannot equal 2, -2, and 3 because it will make the denominators equal zero.

Step 4: Solve

The final step is to solve. Multiply each term by the denominators, cancel out similar factors that are on the numerator and denominator and solve for x.