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**Unformatted text preview: **rrent of a river is c miles per hour. A boat's speed in still water is
12 miles per hour. Write a simplified expression that will represent the
difference in the times required for this boat to travel 150 miles downriver
and upriver.
solution: 12 + c represents the speed of the boat travelling downriver (in miles/hour).
12 − c represents the speed of the boat travelling upriver (in miles/hour).
150 is the time the boat takes travelling 150 miles downriver (in hours).
12 + c
150 is the time the boat takes travelling 150 miles upriver (in hours).
12 − c The difference in these times is the longer time minus the shorter time;
150(12 + c)
150(12 − c)
150 − 150
which simplifies to
−
12 − c
12 + c
(12 − c)(12 + c)
(12 + c)(12 − c)
150(12 + c) − 150(12 − c)
(12 − c)(12 + c)
1800 + 150c − 1800 + 150c
(12 − c)(12 + c)
300c
(12 − c)(12 + c)
Answer: It took 300c
hours longer to go 150 miles upriver.
(12 − c)(12 + c) exercise: Ann and Bob drove separately the 300 km from Kamloops to Banff. They left
at the same time. Ann drove x hours and arrived 1 hour before Bob. Write a
simplified expression that represents how much faster Ann drove. [Answer: 300 km/h
x( x + 1) Unit 5: Day 5 notes - Adding and Subtracting Rational Expressions (Part 2) Page 2 of 2 COMPLEX FRACTIONS
Complex fractions are rational expressions with fractions in the numerator and/or the
denominator.
Complex fractions can be simplified in two ways.
1. Rewrite the numerator and denominator as single fractions and divide them.
2. Multiply the numerator and denominator by the lowest common denominator of the
fractions within.
8+2
5 ; simplify your answer.
example: Evaluate
3 −1
10
Method 1 Method 2 42
5
−7
10 )
)
10(8) + 10 ( 2 )
5
10 ( 3 ) − 10(1)
10 42 ÷ − 7
5
10 80 + 4
3 − 10 40 + 2
55
3 − 10
10 10 (
( 10 8 + 2
5
10 3 − 1
10 ( 42 ) ( − 10 )
5
7 84
−7 −12 1+1
exercise: Simplify a b
1−1
ab −12 exercise: Simplify x − 16
x
2 −1
x −2 [Answers: b + a , − ( x − 2)( x + 4)
b−a
x PRE-CALCULUS 11 Unit 5 – D...

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