Algebra II Section 5 2 Products and Quotients

Algebra II Section 5. 2 Products and Quotients of Rational Expressions

Warm-up •

You’re getting warmer! •

• Rational Expression- quotient of two polynomials • Simplifying a rational expression means factoring and reducing.

• You can reduce any FACTOR in the numerator with any FACTOR in the denominator. • NEVER, NEVER REDUCE TERMS!!!!

• If you have more than one term in the numerator or denominator, dress the expression in parentheses. • Two rules #1 Never go in the dressing room #2 Never take anything out before it is dressed!

In a Nutshell! Factor First, Then Reduce!!!

• A rational expression is undefined if a value of x would make the denominator equal zero. • Set a denominator equal to zero to find xvalues where the expression is undefined

Try these! Page 324 #2 -7

Vintage Math • Recall the rules for multiplying fractions!

Simplify fractions! •

Numerator and Denominator • Always dress them up before you take anything out!

• When multiplying rational expressions#1 Factor all numerators and denominators completely (remember parentheses) #2 Cancel any numerator with any denominator! #3 Multiply what’s leftnumerator x numerator denominator x denominator

Factoring check #1 GCF? #2 Difference of perfect squares? #3 Factorable trinomial? #4 Factor out a -1?

Factor 1 st, then reduce! •

Try these! Pg. 324 #8 -10

More vintage math • Recall rules for dividing fractions-

Factor 1 st, keep, flip, then reduce! •

Try these! • Pg. 324 #11 -14

• If you have an equation with a fraction, simplify the fraction. Sometimes the fraction disappears!

• Solving an equation. • Simplify the fractions in the equation! • When you get your final answer- YOU MUST CHECK IT IN THE ORIGINAL EQUATION! • Any value that results in a denominator of zero is eliminated from the solution set.

• A possible way to eliminate fractions in an equation. Factor and reduce the fraction so the denominator is one

• Extraneous roots- answers to a changed equation that do not work in the original equation.

Try these! • Pg 324 #15 -17

Homework/classwork • Pg. 324 #18 -34, 47 -49