Unit 4 Rational functions

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Unit 4 Rational functions

• 8-6 Solving rational expressions

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Solving Rational Equations

• To solve a rational equation first multiply each
  side by the LCD.
• You must check for extraneous solutions. (A
  solution that doesnt work)

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SOLVE
LCD?
Multiply by LCD
SOLVE
Check for Extraneous solutions. (plug answer into
original problem
4
SOLVE
LCD?
CHECK ??
-1 does not work so there is NO SOLUTION
5
How to solve using the CALC.

• Set equal to zero and graph (have to use
  parenthesis.
• Y2 0
• Find where the graph crosses x-axis (2nd trace
  intersect).

Answer
X0
Answer
X 1, -1
Answer
X -2
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Practice

• Pg 546 8-19(all), 44-52(even)

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Word Problems

• The function below gives the concentration of the
  saline solution after adding x milliliters of
  0.5 solution to 100 milliliters of 2 solution.
• How man ML of the 0.5 solution must be added to
  have a combined concentration of 0.9?

Answer (graph? solve by hand)
X275
8

• You earn a 75 on the first test of the quarter
  how many consecutive 100 test scores do you need
  to bring your test average up to a 95?

Write a rational function. Find when the
rational function will be 95
Answer
You will need to make 100 on the next 4 test to
bring your test average up to a 95
To find the average of something add and divide
by total number
Answer (graph)
9
Distance rate x time
When a problem involves how fast, how far, or
for how long, think about distance equation d
rt

• A plane flies 1850 miles at a speed of 480 mph.
  Find the time of the trip to the nearest
  hundredth.
• On the return trip the plane travels at the same
  speed (480) but a tail wind helps the plane move
  faster. The total flying time for the round trip
  is 7.55 hours. Find the speed x of the tail wind.

Answer
Answer
10
Work Problems

• you have to think of the problem in terms of how
  much each person or thing does in a given amount
  of time

Joe can paint a room in 8 hours and Steve can
paint the same room in 12 hours. How long will it
take the two to paint the room if they work
together?
Working together Mary and Sally can paint a fence
in 5.14 hours. Working alone Mary can paint the
fence in 9 hours. How long would it take Sally to
paint the fence alone?
How much of the job can Joe do in one hour? Steve?
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Practice

• Pg 521 35, 39, 40, 46
• Pg 545 20,36,37,38,39

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A plane leaves Chicago and flies to San Francisco
(1850 miles away) with a headwind The same
plane returns to Chicago with a tailwind. The
round trip took 7.75 hours.If the airplane
cruises at 480 mph, what is the speed of the
wind? (Assume the winds are constant.)
Rate time distance
Time of a trip equals the distance over speed
Xwind speed
San Francisco
Chicago
Solve by Graphing
Zoom fit, x-max to 50
Write an equation
X 35.195