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MTH209 Week 3 Homework Quiz Solution Key

Rational Expressions & Radicals (Chapters 6 of Dugo 2nd Ed)
Section 6.1 Exercises Pages 373-376 Problems 16, 32, 78
Section 6.2 Exercises Pages 381-383 Problems 22, 68, 76
Section 6.3 Exercises Pages 389-391 Problems 20, 64
Section 6.4 Exercises Pages 398-401 Problems 28, 36, 52, 58
Section 6.5 Exercises Pages 406-408 Problems 42
Section 6.6 Exercises Pages 412-413 Problems 30, 42, 50
Section 6.7 Exercises Pages 419-422 Problems 44
Section 6.8 Exercises Pages 428-431 Problems 6, 8

Page 374/16
Which numbers cannot be used in place of the variable in each rational expression? See Example 2 on page 367.
   84
3-2a                 3/2 can’t be used

 

Page 374/32   
Reduce the rational expression to lowest terms.
3m+9w
3m − 6w          3(m+3w)/3(m-2w) = m+3w/m-2w

 

Page 374/78   
Reduce the expression to lowest terms.
4x 2
2x 9                       
2/x^7              

Page 382/22   
Perform the indicated operations.
     3  *   2a+2     
a2  +a       6

 3           *   2*a +2
a^2 + a       2*3

 4      =   2___         
2a^2      a^2

Page 383/68   
Perform the indicated operations.
    −2a2   *   20a
   3a2         15a3  

-2*a*a     *    20*a______
3*a*a          15*a*a*a

-40___   =  -8___
45a^2         9a^2

Page 383/76   
Perform the operations.
x3 − 1  ÷ 9x2 + 9x +9
x2 + 1       x2 − x

x^3-1_____   *  x^2-x
x^2+1               9x^2 + 9x +9

(x^2-1)(x+1)   *  (x+x)(x+x)
(x+1)(x+1)             3(x^2 +3x +3)

x^3-1(x-1)
(x+1)*3(x^2+3x+3)

Page 389/20   
Build the rational expression into an equivalent rational expression with the indicated denominator. See Example 1 page 384.
7b         =             ?
12 c5             36 c8

7b___   = 7b(3c^3)___ = 21bc^3
12c^5       12c^5(3c^3)    36c^8

= 7bc^3
    13c^8

Page 390/64   
Find the LCD for the given rational expression, and convert the rational expression into an equivalent rational expression with the LCD as the denominator. See Example 5, page 388.

    4      ,      5x
x – y      2y – 2x

4(-2)  ,     5____
(x-y)(-2)  2y-2x

-8_____ ,     5____
2y-2x           2y-2x

           
Page 399/28   
Perform the indicated operations.

    3-a      −      a − 5
     3                3

 

Page 399/36   
Perform the indicated operations.

    y      +     y
    4           2

Page 399/52
Perform the indicated operations.

     1      −     2
a − 1           a

Page 399/58
Perform the indicated operations.

     x     +     3
x2 − 1       x − 1

 

Page 407/42   
Simplify each complex fraction. Reduce the answer to lowest terms.

1   +    1
3         y
y     -   3
3          y

1/3 + 1/y (3y)
y/3 – 3/y (3y)

y + 3y/y
y^2 – 9y/y

     y + 3 
y^2 – 9

 

 

Page 412/30
Solve the equation.

     x     =     2
x +3        x − 3

x/x + 3 = 2 (x-3)
x(x - 3) = 2(x + 3)
x^2 - 3x = 2x + 6 
x^2 - 5x + 6 = 0
x – 3 = 0
x = 3
x – 2 = 0
x = 2

Solution x = 2

 

Page 413/42
Solve the equation. Check answers for extraneous solutions in the original equation.

     z     − 1     =                    7
z −2        z+5       z2 +3z −10

z/z-2 – 1/z+5 = 7 / (z + 5)(z - 2)
z(z + 5) -1(z - 2) = 7
z^2 + 5z – z + 5 = 7
z^2 + 4z +2 = 7
z^2 + 4z – 5 = 0
(z + 5)(z – 1) = 0
z + 5 = 0
z = -5
z – 1 = 0
z = 1

-5/-5-2 – 1/-5 + 5 = 7 / -5^2 + 3(-5) -10

1 / 1-2 – 1 / 1+5 = 7 / 1 + 3 - 10

-5 causes 0 in the denominator and is extraneous.

Solution is z =  1

Page 413/50   
Solve the equation. Check answers for extraneous solutions in the original equation.

a + 4    = a + 4
  2              a

a(a + 4) = 2(a + 4)
a^2 + 4a = 2a + 8
a^2 + 2a – 8 = 0
(a + 4)(a – 2) = 0
a + 4 = 0
a = -4
a – 2 = 0
a = 2
a = -4 or 2

2 + 4 / 2 = 2 + 4 / 2
3 = 3

-4 +4 / 2 = -4 + 4 / -4
0 = 0

Solution  = 2

 

Page 420/44   
Fast Food. If four out of five doctors prefer fast food, then at a convention of 445 doctors, how many prefer fast food?
     4   *445 =  356
     5        

4/5 = x/445
5x = 4(445)
5x = 1780
5        5
x = 356

Page 428/6     
Solve the equation for y
y − h = a                     y-h = ax + ak
x+k                              y = ax + ak + h

 

Page 428/8     
Solve the equation for y
y − 1 = − 3
x+3         4                   y – 1 = -3/4(x+3)
                                    y – 1 = -3/4x + -9/4
                                    y = -3/4x + (-9/4) + 1
                                    y = -3/4x – 5/4

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