﻿ Complex Rational Expressions Worksheet - Page 2 | Problems & Solutions
To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free) # Complex Rational Expressions Worksheet - Page 2

Complex Rational Expressions Worksheet
• Page 2
11.
Simplify :
$\frac{\frac{10y}{\left(y+9\right)³}+\frac{9}{y+9}}{\frac{90}{\left(y+9\right)²}+\frac{38}{\left(y+9\right)²}}$. a. b. c. d.

#### 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: $\left(\frac{6}{y}\right)/\left(\frac{5}{x}\right)$ a. $\frac{6y}{5x}$ b. $\frac{5x}{6y}$ c. 30$\mathrm{xy}$ d. $\frac{6x}{5y}$

#### Solution:

(6y)/(5x)

= 6y ÷5x
[Rewrite.]

= 6y x5
[Multiply with the reciprocal.]

= 6x5y

Correct answer : (4)
13.
Simplify: a. b. c. d.

#### 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:
$\frac{\frac{1}{b²}-\frac{1}{ab}}{\frac{1}{ab²}-\frac{1}{a²b}}$ a. $\frac{{\left(a-b\right)}^{2}}{{a}^{3}{b}^{4}}$ b. $\frac{1}{a}$ 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: a. b. c. d.

#### 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: a. b. c. d.

#### 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:
$c$ + $\frac{1}{c+\frac{1}{c}}$ a. $\frac{{c}^{2}+1}{c³+2c}$ b. $\frac{{c}^{3}+2c}{c²+1}$ c. d. $\frac{{c}^{3}+c+1}{c²+1}$

#### 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: a. b. c. d.

#### 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: a. b. c. d.

#### 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: a. b. c. d.

#### 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)

*AP and SAT are registered trademarks of the College Board.