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Complex Rational Expressions Worksheet - Page 2

Complex Rational Expressions Worksheet
  • Page 2
 11.  
Simplify :
10y(y+9)³+9y+990(y+9)²+38(y+9)².
a.
(y² + 172y + 729)128(y + 9)
b.
(9y² + 172y + 729)y + 9
c.
(9y² - 172y + 729)y + 9
d.
(9y² + 172y + 729)128(y + 9)


Solution:

10y(y+9)³+9y+990(y+9)²+38(y+9)²

= [10y+9(y+9)²(y+9)³(90+38)(y+9)²]
[Take LCD in the numerator and the denominator.]

= [9y²+172y+729(y+9)³128(y+9)²]
[Simplify.]

= 9y²+172y+729(y+9)³ ÷128(y+9)²
[Rewrite.]

= [9y²+172y+729(y+9)³ (y+9)²128]
[Multiply with the reciprocal.]

= 9y²+172y+729128(y+9)
[Cancel the common factors.]


Correct answer : (4)
 12.  
Simplify: (6y)/(5x)
a.
6y5x
b.
5x6y
c.
30xy
d.
6x5y


Solution:

(6y)/(5x)

= 6y ÷5x
[Rewrite.]

= 6y x5
[Multiply with the reciprocal.]

= 6x5y


Correct answer : (4)
 13.  
Simplify:
[5 +6x][6 +76x]
a.
6(6x + 5)36x + 7
b.
30x + 3636x + 7
c.
5x + 636x + 7
d.
36x + 730x + 36


Solution:

[5 +6x][6 +76x]

= 5x+6x36x+76x
[Take LCD and simplify the numerator and the denominator.]

= 5x+6x÷36x+76x
[Rewrite.]

= 5x+6x6x36x+7
[Multiply with the reciprocal.]

= 6(5x + 6)(36x + 7)
[Cancel the common factors.]

= 30x + 3636x + 7
[Multiply the numerator by 6.]


Correct answer : (2)
 14.  
Simplify:
1b²-1ab1ab²-1a²b
a.
(a-b)2a3b4
b.
1a
c.
a
d.
- a


Solution:

1b2 -1a b1a b2 -1a2b

= a - ba b2a - ba2b2
[Take LCD and simplify the numerator and the denominator.]

= [a - bab2 ÷a - ba2b2]
[Rewrite.]

= [a - ba b2 .a2b2a - b]
[Multiply with the reciprocal.]

= a
[Cancel the common factors.]


Correct answer : (3)
 15.  
Simplify:
10+9y24y - 12
a.
10y² + 94y - 12y²
b.
10y² - 94y + 12y²
c.
4y - 12y²10y² + 9
d.
10y² + 94 - 12y


Solution:

[10 +9y24y - 12]

= [10y2 + 9y24 - 12yy]
[Take LCD and simplify the numerator and the denominator.]

= [(10y2 + 9y²) ÷ (4 - 12yy)]
[Rewrite.]

= [(10y² + 9y²)  (y4 - 12y)]
[Multiply with the reciprocal.]

= [10y2 + 9y][14 - 12y]
[Cancel the common factors.]

= 10y2 + 94y - 12y2
[Multiply the denominator by y.]


Correct answer : (1)
 16.  
Simplify:
[4(2x - 4)][5x(x² - 4)]
a.
2x + 45x
b.
2x - 45x
c.
5x2x - 4
d.
25x(x - 2)²(x+2)


Solution:

[4(2x - 4)][5x(x² - 4)]

= [42(x - 2)][5x(x - 2)(x + 2)]
[Factor.]

= [[42(x - 2)] ÷ [5x(x - 2)(x + 2)]
[Rewrite.]

= [[42(x - 2)] · [(x - 2)(x + 2)5x]
[Multiply with the reciprocal.]

= 2(x + 2)5x
[Cancel the common factors.]

= 2x + 45x
[Multiply the numerator by 2.]


Correct answer : (1)
 17.  
Simplify:
c + 1c+1c
a.
c2+1c³+2c
b.
c3+2cc²+1
c.
c² + c + 1c² + 1
d.
c3+c+1c²+1


Solution:

This problem has to be done step by step.

= c + 1c +1c

= c + 1c2+1c
[Simplify.]

= c + cc2+1
[1c2+1c = cc2+1.]

= c(c²+1)+cc²+1
[Take LCD.]

= c3+2cc2+1
[Simplify.]


Correct answer : (2)
 18.  
Simplify:
1y + 1y-1y+1y
a.
y³(y + 1)(y² + 1)
b.
y² + 1y³ + y²
c.
y² + 1y4+y3
d.
y² + 1(y + 1)(y³ - 2y)


Solution:

This problem has to be done step by step.

1y + 1y-1y+1y

= 1y + 1y -1y² + 1y
[Simplify.]

= 1y + 1y -yy² + 1
[1y² + 1y = yy² + 1.]

= 1y + 1y³ + y - yy² + 1
[Find LCD.]

= 1y + 1y³y² + 1
[Simplify.]

= 1y + 1 · y² + 1y³
[Multiply by the reciprocal.]

= y² + 1y4 + y³
[Multiply the denominator by y3.]


Correct answer : (3)
 19.  
Simplify: 11x - 9 - 1210 -8x - 9
a.
- 12x + 9710x - 98
b.
- 12x + 11910x - 98
c.
12x + 9710x - 82
d.
- 12x + 11910x - 82


Solution:

11x - 9 - 1210 -8x - 9

= x - 9x - 9· 11x - 9 - 1210 -8x - 9
[The LCD is x - 9, so multiply by x - 9x - 9.]

= 11x - 9 (x - 9) - 12(x - 9)10(x - 9) -8x - 9(x - 9)
[Simplify.]

= 11 - 12(x - 9)10(x - 9) - 8

= - 12x + 11910x - 98
[Distributive property.]


Correct answer : (2)
 20.  
Simplify: 12bb² - 64-11b - 88b - 8+9b + 8
a.
23b + 8817b - 8
b.
b + 8817b + 136
c.
b - 8817b + 136
d.
b - 8817b - 8


Solution:

12bb² - 64 -11b - 88b - 8 +9b + 8

= 12b(b - 8)(b + 8) -11b - 88b - 8 +9b + 8
[Factor.]

= (b - 8)(b + 8)(b - 8)(b + 8)· 12b(b - 8)(b + 8) -11b - 88b - 8 +9b + 8
[The LCD is (b - 8)(b + 8), so multiply numerator and denominator by (b - 8)(b + 8).]

= 12b(b-8)(b+8)(b-8)(b+8)-11b-8(b-8)(b+8)8b-8(b-8)(b+8)+9b+8(b-8)(b+8)
[Distributive property.]

= 12b - 11(b + 8)8(b + 8) + 9(b - 8)

= b - 8817b - 8


Correct answer : (4)

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