Intermediate Algebra

Intermediate Algebra

Section 6 .1 Factoring out the opposite of a common factor . Reduce each expression to lowest terms

78 ) 4x2 2x2 2 88 ) -2x -8 -2 (x 4 ) -2

---- ( ---- --- ------------ ------------ -----

2x9 2x2 x7 x2 2x -8 (x 4 (x-2 ) x-2

Section 6 .2 . Multiplication and division of Rational expressions Perform the indicated operation

68 ) -2a2 20a -40a3 5a3 -8

------- ( ------ ------ ( ------ -----

3a2 15a3 45a5 5a3 9a2

76 ) x3 - 1 9x2 9x 9 (x-1 (x2 x 1 ) 9

(x2 x 1

-------- / ---------------- --------------------- ----------------

x2 1 x2 - x x2 1 x ( x - 1

(x-1 (x2 x 1 x ( x - 1 ) x (x-1 (x-1

--------------------- ( ---------------- ---------------

x2 1 9 (x2 x 1 ) 9 (x2 1

80 ) Solve each problem . Answers could be rational expressions

Henry sold 120 magazine subscriptions in x 2 days . If he sold at the same rate for another week , then how many magazines did he sell in the extra week

Let x number of days For 1 week 7 days ( magazine per day sold

x 2 120 7 ( 1

x 118 days 7 magazines sold in the extra week

Henry sold 120 magazines in 120 days . This means he sells 1 magazine a day

Section 6 .3 . Finding the least Common Denominator

Find the LCD for the given rational expressions , and convert each rational expression into an equivalent rational expression with the LCD as denominator

Converting to the LCD

4 5x 4 5x 4 5x

---- , --------- ---- , --------- LCD : 2 (x-y (y-x --------------- , ---------------

x-y 2y - 2x x-y 2 (y-x 2 (x-y (y-x ) 2 (x-y (y-x

70 ) 3 2b -5 3 2b -5

--------- , -------- , ---------- -------------------- -------- , ------------

4b2 - 9 2b 3 2b2 - 3b (2b 3 (2b - 3 ) 2b 3 b (2b - 3

3 2b -5

LCD : b (2b 3 (2b - 3 ---------------------- ---------------------- , ----------------------

b (2b 3 (2b - 3 b (2b 3 (2b - 3 ) b (2b 3 (2b - 3

Section 6 .4 Addition and Subtraction

Rational expressions with different denominators . Perform the indicated operation . Reduce each answer to lowest terms

76 ) 3 3 3 3 3 [2 (y 2 )] - 3 (2y ) 3 (2y 4 ) - 6y

---- - ------ ---- - ---------- LCD : 4y (y 2 ------------------------ ------------------

2y 2y 4 2y 2 (y 2 4y (y 2 ) 4y (y 2 ) 6y 12 - 6y 12 3 ---------------- ------------ ---------- 4y (y 2 ) 4y (y 2 ) y (y 2

82 ) 4 2 2 4 2 2 4 (n 1 2 (3n 2 (3

---- ----- --------- ---- ----- --------- LCD : 3n (n 1 ---------------------------

3n n 1 n2 n 3n n 1 n (n 1 3n (n 1

4n 4 6n 6 10n 10 10 (n 1 ) 10

------------------- ----------- ----------- -----

3n (n 1 ) 3n (n 1 ) 3n (n 1 ) 3n88 ) Barn Painting . Melanie can paint a certain barn by herself in x days . Her helper Melissa can paint the sane barn by herself in 2x days . Write a rational expression for the fraction of the barn that they complete in one day by working together . Evaluate the expression for x 5

1 2 Evaluation : 1 2

--- x --- x x --- 5 --- 5 5

3 3 3 3 5 10 15 --- --- 5 ----- 5 5 5 3 3 3

Section 6 .5 Complex Fractions . Simplify each complex fraction . Reduce each answer to lowest terms

42 ) 1 1 y 3 y 3

--- --- ------- -------

3 y 3y 3y y 3 3y 1

---------------- ---------- --------------- -------- ------------- ------

y 3 y2 - 9 (y 3 (y-3 ) 3y (y 3 (y-3 ) y-3

--- - --- ------- -------------

3 y 3y 3y

50 ) ab b2 b (a b

---------- --------

4ab5 4ab5 b (a b ) 6a2b4 3a

------------ ---------- -------- ( -------- -----

a b a b 4ab5 a b 2 -------- --------

6a2b4 6a2b4

Section 6 .6 Solving equations with rational expressions . An equation with two solutions

Solve each equation

50 ) a 4 a 4 a 4 a 4 a (a 4 ) - 2 (a 4 a2 4a - 2a -8

------ ------ ----- - ----- 0 ------------------- 0 ------------------ 0

2 a 2 a 2a 2a

a2 2a - 8 (a 4 (a-2

-------------- 0 ------------- 0 (a 4 (a-2 2a

2a 2a

Equation 1 : a 4 2a Equation 2 : a - 2 2a

a - 2a -4 a - 2a 2

-a -4 -a 2

-1 -1

a 4 a -2

64 ) 4w-1 w-1 w-1 4w-1 w-1 w-1 (4w-1 ) - (w-1 (w 2 ) - 3 (w-1

-------- - ----- ----- -------- - ----- - ----- 0 ------------------------------------- 0

3w 6 3 w 2 3 (w 2 ) 3 w 2 3 (w 2

(4w-1 ) - (w2 2w -w -2 ) - 3 (w-1

br ------------------------------------------- 0

3 (w 2

4w - 1 - w2 - 2w w 2 - 3w 3 - w2 4

br ------------------------------------------- 0 ----------- 0 br

3 (w 2 3 (w 2

- (w2 - 4 ) - (w 2 (w-2

------------ 0 --------------- 0 - (w 2 (w-2 3 (w 2

3 (w 2 ) 3 (w 2

Equation 1 : - (w 2 3 (w 2 ) Equation 2 : - (w-2 3 (w 2

-w-2 3w 6 -w 2 3w 6

-w-3w 6 2 -w-3w 6 - 2

-4w 8 -4w 4

-4 -4

w -2 w -1

Section 9 .1 Radicals . Find each root . All variables represent non negative real numbers

Roots of exponent expressions

_____ _______ ____ ______ ___

26 ) V m6 V m4 (m2 mV m4 mV m2 (m2 m2Vm2 m3

Use product rule for radicals to simplify each expression

3______ 3 _________ 3 _____ 3 ________ 3 _____ 3 _____

V 5b9 V5b3 (b6 bV5b6 bV5b3 (b3 b2V5b3 b3V 5

Use the product rule to simplify 4 ___ 4 ______ 4 _____

V 32 V16 (2 2V 2

Simplify each radical . All variables represent positive real numbers Using the quotient rule for radicals

_____

V 9 3 3 1

------ ----- ( ----- ---

144 12 3 491 ) Use the product and quotient rules to simplify . All variables represent positive real numbers

_____ _____ ___

V 27 V 9 (3 3 V 3

----- ------ 4

16 16

Learning team

Either perform the indicated operation or solve the equation , whichever is appropriate 3 5 3 5 3x - 5 (10 ) 3x - 50

--- --- --- - --- 0 ------------- 0 --------- 0 3x - 50 10x

10 x 10 x 10x 10x

3x - 10x 50 -7x 50 x - 50 -7 7

114 ) 4 1 4 1 4 (2 (a-1 ) 8 a - 1 a - 7

------- ------ ------------ -------- -------------- ------------- -------------

a2 - 1 2a 2 (a 1 (a-1 ) 2 (a 1 ) 2 (a 1 (a-1 2 (a 1 (a-1 ) 2 (a 1 (a-1

Simplify each radical expression . Assume all variables represent positive real numbers

______ ________ ____

V 12a3 V4 (3 (a2 (a ) 2a V 3a

------ ----------- 5

25 25

Reference

Loquinte , D .M Tarepe , D . A . Freshmen College Algebra (2000 edition Philippines : MPSC Publishing House

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