Name
Class
11-1
Date
Practice
Form G
Simplifying Rational Expressions
Simplify each expression. State any excluded values. 1.
q11 2. q 1 4q 1 3
6p 2 36 p 2 6 18 3
1 q 1 3;
x11 1 4. 2 ; x u 1, 21 x 21 x21
7.
x2 2 144 3x2 2 36x x 1 12 3x ;
10.
7(d2 1 2) ; 2(3d 2 1)
d u 0, 13
9.
5y 1 11 ; 3
3x2 1 19x 2 14 x2 2 49 3x 2 2 x27;
n u 0, 4
25y2 2 121 11. 15y 2 33
7d3 1 14d 6d2 2 2d
3b 2 6 3 6. 2 ; b u 22, 2 b 24 b12
n2 2 n 2 12 n2 2 4n n 1 3 n ;
8b5 b , b u 0 64b4 8
q u 23, 21
56c 2 14 7 1 5. 24c 2 6 3 ; c u 4
8.
x u 0, 12
3.
12.
y u 11 5
x u 7, 27
99q2 2 2q 2 1 9q 2 1
11q 1 1, q u 19
13. The length of a rectangle is 3h 1 2 and the width is 9h 1 6. What is the ratio
of its length to its width? Simplify your answer. 13; h u 223
14. The length of a rectangle is x 2 2. Its area is 2x 2 4. What is a simplified expression for the width? 2 15. The area of a rectangle is x2 2 9. Its width is x 2 3. What is a simplified
expression for the length? x 1 3 16. Writing Why must the denominator of a rational expression not be equal to 0? It is undefined; can’t divide by 0 and can’t graph a 0 denominator 17. The area of a rectangle is 16a2 . The length is 2a. What is a simplified expression for the the width? 8a
18. Are the given factors opposites? Explain. a. 3d 2 7; 7 2 3d yes; 21(3d 2 7) 5 (23d 1 7) 5 (7 2 3d) b. 2y 1 4; y 1 4 no; (21)(2y 1 4) 5 (y 2 4) u (y 1 4) c. 27 1 8x; 227 2 8x yes; (21)(27 1 8x) 5 (227 2 8x)
p(2x)2 19. The ratio of the area of a small circle to a larger circle is . Simplify the p(6x)2 expression. 19; x u 0
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Name
Class
11-1
Date
Practice (continued)
Form G
Simplifying Rational Expressions
20. A pilot packed two rectangular suitcases for her trip to Hawaii. Both hold the
same volume of clothes. Her green suitcase has a length of 2y 1 4, a width of y 1 1, and a height of 4y. Her blue suitcase has a length of 8y2 2 6y and a width of 2y. What is a simplified expression for the height of the blue suitcase? Show your work. 2(y 1 2)(y 1 1) y(4y 2 3)
; y u 0, 13
21. The numerical area of a circle with radius c is equal to the numerical volume
of a sphere with radius S. What is the radius of the sphere in terms of c? Show 4 your work. (Area circle 5 pr2 . Volume sphere 5 3 pr3 ). 3
"34 c 2
Simplify each expression. State any excluded values. 22.
x2 2 9 x 1 3 ; x u 0, 3 2x2 2 6x 2x
23.
n2p2 p; n u 0, p u 0 n2p
24.
2x2 1 17x 2 9 2x 2 1 x 2 9 ; x u 9, 29 x2 2 81
25.
4d4 2 6d3 2 4d2 4d2 1 2d; d u 0, 2 d2 2 2d
26.
11y2 1 35y 2 36 y2 2 16
27.
6a5b 1 4ab3 1 3a4c 1 2b2c 2ab 1 c
11y 2 9 y24 ,
3a4 1 2b2; 2ab 1 c u 0
y u 4, 24
mi 28. Your brother’s car is traveling 40 faster than h
your car. During the time it takes you to go 150 mi, your brother goes 450 mi. Make a table with the information and find the speeds. Your speed 20 mi/h; Your brother’s speed 60 mi/h
Distance You
150
r
Your brother
450
r à40
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Rate
Time 150 r
450 r à40
Name
11-1
Class
Date
Practice
Form K
Simplifying Rational Expressions
Simplify each expression. State any excluded values. 1.
3n 2 15 n 2 5 4 12
2.
y12 1 ; y u w2 3. 2 y 24 y22
12t 8 t2 ;tu0 36t 6 3
15a 2 50 3a 2 10 4. 10a 1 35 2a 1 7 ; a u 23.5
5.
q2 2 16 q 2 4 ; q u 0, 24 7q2 1 28q 7q
6.
7.
m3 1 9m m2 1 9 ; m u 0, 12 6m2 2 3m 6m 2 3
9z2 2 36 3z 2 6 8. 12z 1 24 4 ; z u 22
5x2 1 x 2 6 5x 1 6 x 1 1 ; x u w1 x2 2 1
9. The length of a rectangle is 8n 1 24 and the width is 12n 1 28. What is the
ratio of its length to its width? Simplify your answer.
2n 1 6 3n 1 7
10. The area of a rectangle is x2 1 6x 2 16. Its width is x 2 2. What is a simplified expression for its length? x 1 8
11. Writing Describe how you determine what values should be excluded when
simplifying a rational expression. Explain why this must be done. Set each factor with a variable in the denominator equal to zero and solve for the variable. The denominator cannot equal zero. 12. Are the given factors opposites? Explain. a. 5x 2 2; 2 2 5x yes, if you factor a negative out of one of the factors, the factors are equivalent. b 2t 1 10; t 1 10 no, if you factor a negative out of one of the factors, the factors are not equivalent. c. 102 1 11d; 2102 2 11d yes, if you factor a negative out of one of the factors, the factors are equivalent.
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Name
Class
11-1
Date
Practice (continued)
Form K
Simplifying Rational Expressions
13. A mother is packing away winter clothes into two rectangular tubs. Both hold
the same volume of clothes. The first tub has a length of 2b 1 5, a width of b 2 3, and a height of 4b. The second tub has a width of 4b2 1 10b and a length of b 2 3. What is a simplified expression for the height of the second tub? Show your work. (2b 1 5)(b 2 3)(4b) 5 h(4b2 1 10b)(b 2 3) (2b 1 5)(b 2 3)(4b) (2b)(2b 1 5)(b 2 3)
5h
25h
Simplify each expression. State any excluded values. 14.
x2 2 121 x2 2 121 ; x u 0, 3 3x2 2 9x 3x2 2 9x
v3w3 15. 2 3 v; v u 0, w u 0 v w
16.
5x2 2 41x 1 42 x2 2 49
17.
2t4 1 t3 2 28t2 t(2t 2 7); t u 0, 24 t2 1 4t
18.
9m2 2 32m 2 65 9m 1 13 m 1 5 ; m u w5 m2 2 25
19.
8a2 2 12a 2 36 4(2a 1 3) ; a u w3 a 1 3 a2 2 9
5x 2 6 x 1 7;
x u w7
x2 2 81 20. Writing Is x 2 9 the same as x 1 9? Explain. 2 (x 1 9)(x 2 9) 81 5 x 1 9, but x cannot equal 9 in the first expression. No; xx 2 29 5 x29
21. Reasoning Is y 5 4 an acceptable value for the expression
Explain.
3y2 2 10y 2 8 ? y2 2 16
No; 42 2 16 5 0; This would make the denominator equal to 0.
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