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Complex Rational Expressions Worksheet - Page 3

Complex Rational Expressions Worksheet
  • Page 3
 21.  
Simplify: x + 9x+90x + 1010x - 1+89(x + 10)²
a.
10(x³+20x²+109x+90)10x³+199x²+980x-11
b.
10(x³+20x²+109x+90)10x³+199x²+69x+11
c.
9(x³+20x²)199x²+980x-11
d.
9(109x+90)10x³+199x²


Solution:

x+9x+90x+1010x-1+89(x+10)²

= (x+10)²(x+10)² · x+9x+90x+1010x-1+89(x+10)²
[The LCD is (x + 10)2, so multiply numerator and denominator by (x + 10)2.]

= x(x+10)²+9x(x+10)²+90(x+10)10x(x+10)²-(x+10)²+89

= x(x²+20x+100)+9x(x²+20x+100)+90(x+10)10x(x²+20x+100) - (x²+20x+100)+89
[Simplify.]

= 10x³+200x²+1090x+90010x³+199x²+980x-11
[Distributive property.]

= 10(x³+20x²+109x+90)10x³+199x²+980x-11


Correct answer : (1)
 22.  
Simplify: 7a(a+3)3+1(a+3)11(a+3)2+9(a+3)2
a.
a+720a+60
b.
a+311a+33
c.
a²+13a+99a+27
d.
a²+13a+920a+60


Solution:

7a(a+3)3+1(a+3)11(a+3)2+9(a+3)2

= (a+3)³(a+3)³(7a(a+3)³+1(a+3)) / (11(a+3)²+9(a+3)²)
[The LCD is (a + 3)3, so multiply numerator and denominator by (a + 3)3.]

= [7a(a+3)³(a+3)³+1a+3(a+3)³] / [11(a+3)²(a+3)³+9(a+3)²(a+3)³]
[Distributive property.]

= 7a+(a+3)²11(a+3)+9(a+3)
[Simplify.]

= 7a+a²+6a+911a+33+9a+27
[Write (a + 3)2 as a2 + 6a + 9.]

= a²+13a+920a+60


Correct answer : (4)
 23.  
Simplify: 9a-71-8a-7
a.
9a + 1
b.
9a + 15
c.
9a - 15
d.
15a - 9


Solution:

9a-71-8a-7

= a-7a-79a-71-8a-7
[The LCD is a - 7, so multiply by a - 7.]

= 9a-7(a-7)(a-7)-8a-7(a-7)
[Distributive property.]

= 9a-15
[Simplify.]


Correct answer : (3)
 24.  
Simplify:
1+8a+7a²7a+35
a.
a+11+5a
b.
7a(1+5a)(a+1)(a+7)
c.
(a+1)(a+7)7a(1+5a)
d.
(a+1)(a+7)(7+5a)


Solution:

1+8a+7a²7a+35

= a²a²1+8a+7a²7a+35
[The LCD is a2, so multiply by a2.]

= a²+8a+77a+35a²
[Distributive property.]

= (a+1)(a+7)7a(1+5a)
[Factor.]


Correct answer : (3)
 25.  
Simplify: 114b-24-5b+655b-30+6b+6
a.
-9b+18628b-120
b.
-9b-18628b+120
c.
9b+18628b-120
d.
9b-18628b-120


Solution:

114b-24-5b+655b-30+6b+6

= 114(b-6)-5b+655(b-6)+6b+6

11(b+6)-5×4(b-6)4(b-6)(b+6)5(b+6)+6×5(b-6)5(b-6)(b+6)

11(b+6)-20(b-6)5(b+6)+30(b-6) · 5 / 4
[Cancel common factors.]

= 55(b+6)-100(b-6)20(b+6)+120(b-6)
[Distributive property.]

= -45b+930140b-600
[Simplify.]

= -9b+18628b-120
[Simplify.]


Correct answer : (1)
 26.  
Simplify:
1009x-99-9x+119510x-110+9x+11
a.
9(37x+11)2(19x+1991)
b.
92
c.
9(19x+1991)2(37x+11)
d.
2(19x+1991)9(37x+11)


Solution:

1009x-99-9x+119510x-110+9x+11

= 100(x+11)-9[9(x-11)]9(x-11)(x+11)95(x+11)+9[10(x-11)]10(x-11)(x+11)
[Take LCD of numerator and denominator.]

= 100x+1100-81x+8919(x-11)(x+11)95x+1045+90x-99010(x-11)(x+11)
[Simplify.]

= 19x+19919(x-11)(x+11)185x+5510(x-11)(x+11)
[Simplify.]

= 19x+19919(x-11)(x+11) ÷185x+5510(x-11)(x+11)
[Rewrite.]

= 19x+19919(x-11)(x+11) 10(x-11)(x+11)185x+55
[Multiply by the reciprocal.]

= 10(19x+1991)9(185x+55) = 10*1(19x+1991)9*5(37x+11)
[Divide out the common factor.]

= 2(19x+1991)9(37x+11)
[Divide out the common factor.]


Correct answer : (4)

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