10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
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Lesson goal ‐ You will be able to simplify when multiplying and dividing rational functions by factoring and “cancelling out” common factors. NOTE: You will need a lot of paper to properly do these type of problems. Don’t try and fit it all on the notes. Simplified form is when after factoring the numerator and denominator, there are no common factors other than 1. Also, the simplified form is often left in factored form. The property can be illustrated as follows: ·
Examples : ·
Note: Simplifying rational expressions usually requires 2 steps: ‐ Factor numerator and denominator completely ‐ Divide out (cancel ) common factors in numerator and denominator Examples: You try – 10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
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Multiplying rational expressions – Two Options: Long way ‐ Same as multiplying numeric fractions, that is multiply the numerators; multiply the denominators; write new fraction; then simplify if possible. Short way‐ Simplify and cross simplify common factors before multiplying numerators and denominators. May look a little messy, but keeps the numbers smaller and saves work. Examples‐ ·
Long way ‐ Short way‐ ·
10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
3
Multiplying binomial and trinomial rational expressions‐ Here you definitely want to factor and simplify before you multiply the numerator and denominator. Also the simplified expression is often left in factored form. Examples‐ ·
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You try‐ ·
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10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
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Dividing rational expressions‐ Same as above only remember when you divide fractions, you actually multiply by the reciprocal of the term behind the division sign. ·
Examples‐ x
4x
5x
21
15
x
3x 70
100
x
·
3
13
6
10
3
2
·
10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
You try‐ x
4x
5x
20
x
2x
3x
6x
5
2x
6x 8
2x
5x 5
10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
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Practice‐ 10.4 –Multiply and Divide Rational Expressions Write your questions and
thoughts here!
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Application Problems 1. The surface area S and the volume V of a cylindrical can are given by 2
and where r is the radius and h is the height. Write and simplify an expression for the efficiency ratio . 2
2. A fuel storage container is shaped like a cylinder with a hemisphere on each end. The length of the cylinder is l and the radius of each hemisphere is r. Show that the ratio of the surface area to the volume of the container is given 2
4
and .