Ch 3 additional practice rational expressions vs equations PDF

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Algebra 2

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Simplifying Rational Expressions vs Solving Rational Equations

A common error is to confuse an equation, such as

x x   5 , with an expression involving an operation, such as 2 3

x x  . Equations are solved for a numerical answer, while problems involving operations result in simplified 2 3 expressions. Simplifying an Expression Involving an Operation

Solving an Equation Solve:

x x   5 2 3

(Look for the equal sign!)

Multiply each side by the LCD, 6.

Add.

x x  2 3

(There is no equal sign!)

Write both equations with the LCD, 6.

x x 6     6 5   2 3

x x  2 3 x 2

x  x  6    6    6  5  2  3 



3x  2 y  30



3x 2x  6 6



3x  2 x 6

5 x  30 x  6

The solution set is {6} .



5x 6

Identify each exercise as an expression or an equation. Then simplify the expression by performing the indicated operation, or solve the equation, as appropriate. You may wish to do your work on a separate sheet to have more space. 1)

x x  5 2 4

1 1  x y 4) 1 1  x y

2)

4 x  20 ( x  5) 2  2 x  25 10

3)

6 4  7x x

5)

5 52 3   7t 7 t

6)

x5 1 x 2   3 3 5

7 5 7)  6x 8x

4 8 8)  0 x x 1

6 1  x x 1  9) 2 4  x x 1

10)

8 7  r  2 4r  8

11)

x 2y  x y xy

12)

3 p2  6 p p2  4  p 5 8 p  40

13)

x 2 5 9 8  4x

14)

a  4 11 a 1   3 6 2

15)

b 2  b  6 b 2  8b  16 b 2  2b  8 3b  12

16)

10z 2  5z 2z 2  5z  3  2 3z 3  6 z 2 z  z 6

17)

5 3  2 x  2x x  4

18)

3 1 7   t 1 t 2

21)

4 y 2 13 y  3 4 y 2  11y  3  2 y2  9 y  9 6 y2 5 y  6

24)

6 z 2  5z  6 12z 2  17 z  6 6 z 2  5z  6 12z  z  6

27)

2 3 3   y 1 y2  y  2 y  2

5 3  x y 19) 9 x 2  25 y 2 x2 y

22)

8 8 2   3k  9 15 5k  15

20)

2

2 5 4   a  2a  3 3  3a 3a  9 2

23)

3r 6 1  r2 r2

2 1 25)  3 x x 3

t 1  t 4 26) t 4 1 t

7 3 28)  2 2 2x  8 x x  16

3 3 2 29)  2  y 3 y 5 y  6 y  2

5 k 1 2 3k  k

2k  30)

Answers:

2( x  5) 5

1) equation; {20}

2) expression;

 1 5) equation;    2

6) equation;  7

3) expression; 

7) expression;

9) expression;

5x 1 2( x 1)

12) expression;

24 p p2

13) expression; 

16) expression;

5 3z

17) expression;

19) expression;

x 3x  5 y

20) equation;  13

23) equation; No Solutions

26) expression;

t 2 8

29) equation; No Solutions

10) expression;

24) expression;

43 24x

25 4(r  2)

5 36

2 x  10 x( x  2)( x  2)

2z  3 2z  3

27) equation;  10

30) expression;

k(2 k 2  2 k 5) (k  1)(3k 2  2)

22 7x

4) expression;

y x y x

8) equation; 1

11) expression;

x 2  xy  2y 2 ( x  y)( x  y)

14) equation; 0

15) expression;

b 3 3

1  18) equation;  , 2  7 

21) expression;

3y  2 y3

25) expression;

1 1 or x 3 3x

28) expression;

13x  28 2x (x  4)(x  4)

5  22) equation;   4 ...