Pre‐Calculus 11 Chapter 6 – Rational Expressions and Equations Name: _______________________________ Date: ____________ 1. Simplify and determine the NPV. 35a 2b3c 4
a)
40abc 7
7 ab 2

NPV : a  0, b  0, c  0 8c 3
6x2  8x
c)
4x
3x  4

NPV : x  0 2
a 2  10ab  24b 2
e)
a 2  36b 2
 a  4b  NPV : a  6b 
 a  6b 
12  3m
20  5m
b)

d)

f)

3
5
NPV : m  4 m 2  2mn  3n 2
3m 2  9mn
 m  n
3m
NPV : m  0, m  3n 2 x 3  28 x 2  102 x
18 x  2 x 3
 x  17 
  x  3
NPV : x  0,  3, 3 2. Simplify and determine the NPV. a)
 2m 
2
10m 15m


5n
8n  4n 2
16m 2

15
NPV : m  0, n  0 b)

2 x 2  3 x  20 2 x 2  15 x  18

2 x 2  5 x  12 2 x 2  7 x  30
 x  4
 x  4
NPV : x  4,
5 3
, , 6 2 2
3x
x 1
x
3x 
x 1
2x 1 
c)
d)

2x2  4x  1
x  3x  2 
3 y2  3y
y 1
2 y 1 3y 1
y 1
2y 5 

5
3y2  2 9a 2  42ab  49b 2 4a 2  25b 2
2a  5b
e)
 2
 2
2
2
2
2a  13ab  20b 9a  49b 3a  19ab  28b 2
5b
7b
 3a  7b NPV : a   , a   , a  4b 2
3
2 x 2  5 xy  2 y 2 x 2  9 y 2 3x 2  11xy  6 y 2


f)
3x 2  8 xy  3 y 2 x 2  4 y 2 2 x 2  3xy  2 y 2

 x  2 y  2 x  y 
 x  3 y  3x  2 y 
NPV : x  3 y, x  2 y, x  
2y
y
y
,x ,x 3
2
3
3. Simplify and state all NPVs. 6 x  11y 3 x  16 y
a)

9x
6y
9 x 2  36 xy  22 y 2

18 xy
7x
4x
c)
 2
2
x  x  12 x  2 x  3
3x

 x  4  x  1
e)
d)

3a  2
5a  4

a  10a  21 15  2a  a 2
2
2  a 2  22a  9 
 a  7  a  3 5  a 
5m  25
2m  5
 2
2m  13m  15 m  4
2

2x  3y2
5x2  2 y
3
b)
8 xy
6 x2
6 x 2  92 x 2 y  9 xy 2  8 y 2

24 x 2 y
m  4m  5
 m  2  m  2  2m  3
2
f)
3x  y
x  2y
2x  y


2 x 2  11xy  21 y 2 2 x 2  11xy  12 y 2 x 2  3 xy  28 y 2

 x 2  4 xy  15 y 2
 x  7 y  2 x  3 y  x  4 y 
4. Solve. x  15 2 x  1
a)
 
x
5
5
5
x 7
c)
1
4

1 x  2 2x 1
3
x
, 3 2
1
e) x 
 4 x4
x  5,  3 b)
2x 1 4x  3

3x  2 6 x  5
x
1
5
d)
9x2
4x
x


2
x  25 x  5 x  5
x  0,
15
4
f)
3x  2 3x  1 1

 2x 1 x 1 3
x  2,
5
7
5. The average speed of an airplane is five times as fast as the average speed of a passenger train. To travel 2000km, the bus requires 20 hours more than the plane. Determine the average speeds of the train and the plane. Train : 80 km ; Plane : 400 km h
h
6. The average speed of an express train is 40 km/h faster than the average speed of a bus. To travel 1200km, the bus requires 50% more time than the train. Determine the average speeds of the train and the bus. Bus : 80 km ; Train :120 km h
h
7. Each week, Angela flies her small plane 500 km from Lethbridge to Moose Jaw. After a brief stopover, she returns to Lethbridge. On both trips, the air speed is 180 km/h. On the flight out there is a constant 20 km/h tail wind, and on the return trip a constant head wind of the same speed. Calculate the time needed for a round trip. time : 5
5
hours 8