Restrictions on the Domain

RATIONAL EXPRESSIONS NAME

Restrictions on the Domain

· Also called Exclusions

· Restrictions come from the denominator only.

· We restrict out the values that would have made the denominator equal zero, which would have in turn caused division by zero which is not possible.

· Factor, Restrict, Cancel IN THAT ORDER

o Never cancel before finding restrictions.

· Monomial variable factors give restriction “≠ 0”

· Polynomials must be factored first. This gives restriction by setting the binomial factor ≠ 0 and then solving.

Simplifying/Canceling

· Simplifying/canceling can only be done with factors, not with individual terms.

· FACTOR FIRST!!!!

Multiplying Rational Expressions

· Although the topic is multiplication, you will do very little actual multiplying.

o Multiply out if there were some monomial factors that can be combined.

o Multiply out if the problem is a multiple choice question with the answers multiplied out.

o Otherwise, leave the factored products as your answer.

· FACTOR, FACTOR, FACTOR – Only factors can be cancelled, not terms.

· Read the directions first to see whether we are assuming the denominator is not equal to zero. If this assumption is not being made, then you will need to find restrictions before canceling.

· Once everything is factored, cancel out like factors and write down what remains.

Dividing Rational Expressions

· WRITE, CHANGE, FLIP

· After rewriting as the appropriate multiplication problem, follow the same rules from above.

Adding/Subtracting Rational Expressions With Common Denominators

· If you already have common denominators, add/subtract the numerators accordingly and then FACTOR BOTH sides of the fraction.

· Cancel if the same factor appears on both sides of the fraction.

Adding/Subtracting Rational Expressions WITHOUT Common Denominators

· Factor the denominators first and find the common denominator.

· Multiply top and bottom of each fraction by what was missing from its denominator.

· Combine numerators and then factor the sum/difference to see if simplification is possible.

Solving Rational Equations

· FACTOR denominators to find LCM.

· Find restrictions.

· Multiply each term by the LCM to clear fractions out.

o Notice the difference in solving equations as opposed to just doing addition/subtraction.

· Solve equation.

· Check for extraneous solutions.

o Use the ORIGINAL problem to do the check.

· Write solution set.