Math 901: Algebra I Unit 1 Test Study Guide

Math 909 Algebra I Unit 9: Rational ExpressionsTest Study Guide1. Identify the excluded value(s) of an expression – what value(s) is(are) NOTin the domain of the expression.2. Simplify rational expressions to lowest terms.• Monomial divided by monomial. Apply properties of exponents.• Binomial divided by binomial. Factor first, if possible.• Convert complex fractions to a simple fraction. Multiply numerator anddenominator by the lowest common denominator (LCD).3. Add algebraic fractions (rational expressions) by finding the LCD,converting each fraction to a fraction with the LCD and then adding thenumerators.4. Subtract algebraic fractions using the same process as in #3 above.5. Find the lowest common denominator of fractions with binomials in thedenominator. Be able to factor them in order to recognize common factors.6. Multiply rational expressions. Use factoring to simplify.7. Divide rational expressions. Apply properties of exponents to simplify.Remember that dividing is the same as multiplying by the reciprocal.8. Solve equations involving rational expressions. If desired, multiply by theLCD to simplify the equation. If the equation is a proportion, you may alsocross multiply to solve.9. Solve inequalities involving rational expressions. Do them the same way asequations, except if you multiply or divide by a negative number, theinequality symbol must be switched around.10. Solve an equation involving a rational expression for a variable in terms ofother variables.11. Write an expression for the amount of work done by a person. Forexample, if a person can do a certain job in 30 minutes, he can do 1/30 ofthe job in 1 minute. If he works for x minutes, 1/30 x or x/30 wouldrepresent the amount of work he can do in x minutes.12. Solve a verbal problem in which two people work together to complete 1job.13. Solve a verbal problem to find two consecutive odd or even numbers.14. Find the ages of two people using some given information.15. Solve a percentage problem to find how many pounds of a certain ingredientare in a solution.

16. Solve a percent problem to determine how much water must be added todilute a solution from a given percentage to a lesser given percentage.17. Find the rate at which a person must travel in order to complete a roundtrip in a given amount of time. Remember, distance = rate X time,time = distance/rate, and rate = distance/time.