Download Math 117: Test 2

Math 117: Test 2
Jennifer Riddell
Section 5.1 Exercise 40
Write each expression in simplest form.
=
3(a  4)
 3(4  a)
3


(4  a)( 4  a) (4  a)( 4  a) 4  a
Section 5.2 Exercise 40
Divide the following fractions.
= Factor each one:
r2
+2rs
-15s2
= (r-3s) (r+5s)
r3 +5r2s = r2(r+5s)
r2 -9s2 = (r-3s) (r+3s)
Flip the second and multiply:
(r-3s)(r+5s)/(r^2)(r+5s) * 5r^3 / (r-3s)(r+3s)
= 1/(r^2) * 5r^3 /(r+3s)
= 5r/(r+3s)
Section 5.3 Exercise 40
Add or subtract as indicated. Express your results in simplest form.
=
2 x  6 2( x  3)

2
x3
x3
Section 5.4 Exercise 60
Add or subtract as indicated. Express your result in simplest form.
=
Factor the bottoms:
2a/(a-4)(a+3) – 3/(a-4)(a+2)
Common denom:
2a(a+2)/CD – 3(a+3)/CD, where CD = (a-4)(a+3)(a+2)
Subtract:
(2a(a+2) – 3(a+3))/CD
= (2a^2 + 4a – 3a – 9) / CD
= (2a^2 + a – 9) / CD
= (2a^2 + a – 9) / (a-4)(a+3)(a+2)
Section 5.5 Exercise 60
Solve and check each of the following equations for x.
Factor the second term:
5x/(x-4)(x+3)
Make everything get a common denom:
X(x+3)/CD = 5x/CD – 3(x-4)/CD
Multiply by CD:
X(x+3) = 5x – 3(x-4)
X^2 + 3x = 5x – 3x + 12
Combine:
X^2 + x –12 = 0
Factor:
(x-3)(x+4) = 0
x = 3 or –4
Check:
3/(3-4) = 3/-1
(5*3)/(3^2-3-12)-3/(3+3) = -3
Check:
-4/(-4-4) = 0.5
(5*-4)/(-4^2-(-4)-12) – 3/(-4+3) = 0.5
x = 3 or -4
Exercise 70
Solve the equation for x.
=
Factors 9 and 30 have greatest common factor of 3. Reducing fraction.
It becomes
x
3

10 10
Move these terms to the left -
It now becomes
3
10
x
3

0
10 10
Solved linear equation
x
3

 0 equivalent to 0.1·x-0.3=0
10 10
Solution x=3
Section 5.6 Exercise 20
Science and medicine. A small business jet took 1 h longer to fly 810 mi on the
first part of a flight than to fly 540 mi on the second portion. If the jet’s rate was
the same for each leg of the flight, what was the flying time for each leg?
In 1 hour, they went 810-540 miles
= 270 miles
Therefore the times were:
540/270 = 2 hours
and
810/270 = 3 hours
Exercise 30
Business and finance. If 342 cups of coffee can be made from 9 lb of coffee,
how many cups can be made from 6 lb of coffee?
Proportion:
342/9 = x/6
Cross multiply:
9x = 6*342
x = 6*342/9
x = 228 cups
Section 5.7 Exercise 20
Simplify each complex fraction.
Get common denoms (xy):
1/xy + 2y/xy
__________
3x/xy – 1/xy
Combine:
(1+2y)/xy
__________
(3x-1)/xy
Remove the xy:
(1+2y)/(3x-1)
Exercise 30
Take the area divided by the length:
Flip the length and multiply:
2(3x-2)/(x-1) * (x-2)/(3x-2)
Cancel:
2/(x-1) * (x-2)
= 2(x-2)/(x-1)