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
- Slides: 29