To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Complex Rational Expressions Worksheet

Complex Rational Expressions Worksheet
  • Page 1
 1.  
Simplify:
6xx²+4x+45x+2+6x+2
a.
6x11x+22
b.
6x11x+2
c.
11x+226x
d.
6x11x-2


Solution:

6xx²+4x+45x+2+6x+2

6xx²+4x+45x+2+6x+2 = 6x(x+2)(x+2)5x+2+6x+2
[Factor x2 + 4x + 4.]

= 6x(x+2)(x+2)5(x+2)+6(x+2)(x+2)(x+2)
[Take LCD of (x + 2) and (x + 2).]

= 6x(x+2)(x+2)11x+22(x+2)(x+2)
[Simplify.]

= 6x(x+2)(x+2) ÷11x+22(x+2)(x+2)
[Rewrite.]

= 6x(x+2)(x+2) (x+2)(x+2)11x+22
[Multiply by the reciprocal.]

= 6x11x+22
[Divide out the common factor.]


Correct answer : (1)
 2.  
Simplify:
365x-35-5x+7336x-42+5x+7
a.
2(11x+427)35(3x+1)
b.
352
c.
35(11x+427)2(3x+1)
d.
35(3x+1)2(11x+427)


Solution:

365x-35-5x+7336x-42+5x+7

= 36(x+7)-5[5(x-7)]5(x-7)(x+7)33(x+7)+5[6(x-7)]6(x-7)(x+7)
[Take LCD of numerator and denominator.]

= 36x+252-25x+1755(x-7)(x+7)33x+231+30x-2106(x-7)(x+7)
[Simplify.]

= 11x+4275(x-7)(x+7)63x+216(x-7)(x+7)
[Simplify.]

= 11x+4275(x-7)(x+7) ÷63x+216(x-7)(x+7)
[Rewrite.]

= 11x+4275(x-7)(x+7) 6(x-7)(x+7)63x+21
[Multiply by the reciprocal.]

= 6(11x+427)5(63x+21)
[Divide out the common factor.]

= 2(11x+427)35(3x+1)
[Divide out the common factor.]


Correct answer : (1)
 3.  
Simplify:
4xx²+8x+163x+4+2x(x+4)²
a.
8x + 165x + 12
b.
4x5x + 12
c.
5x + 124x
d.
4x8x + 16


Solution:

4xx²+8x+163x+4+2x(x+4)²

= 4x(x+4)²3x+4+2x(x+4)²
[Factor.]

= 4x(x+4)²3(x+4)+2x(x+4)²
[Take LCD of the denominator.]

= 4x(x+4)² ÷5x+12(x+4)²
[Simplify and rewrite.]

= 4x(x+4)² (x+4)²5x+12
[Multiply by the reciprocal.]

= 4x5x + 12
[Multiply with the reciprocal.]


Correct answer : (2)
 4.  
Simplify:
- 3[(b+12a)]
a.
- a(ab + 3)
b.
- 3a(ab + 12)
c.
3a(ab + 12)
d.
- 3a(ab + 12)


Solution:

- 3[b + (12a)]

= - 3(ab + 12a)
[Take LCD and simplify the denominator.]

= - 3 ÷ ab + 12a
[Rewrite.]

= - 3 · aab + 12
[Multiply with the reciprocal.]

= - 3aab + 12


Correct answer : (4)
 5.  
Simplify:
85+xy
a.
85y+x
b.
8y5y+xy
c.
85y+xy
d.
8y5y+x


Solution:

85+xy

= yy85+xy
[The LCD is y, so multiply by y.]

= 8y5y+xyy
[Distributive property.]

= 8y5y+x


Correct answer : (4)
 6.  
Simplify:
(10+x+10x-11)(11-x-909x-99)
a.
- x²-x-1009x²-198x+1179
b.
x²+21x+100x²-22x+131
c.
x²-x-100x²-22x+131
d.
- x²-x-100x²-22x+131


Solution:

(10+x+10x-11)(11-x-909x-99)

= 10(x-11)+x(x-11)+10x-1111(9x-99)-x(9x-99)-909x-99
[Take LCD in the numerator and the denominator.]

= (10x-110+x²-11x+10x-11)(99x-1089-9x²+99x-909x-99)
[Simplify.]

= x²-x-100x-11-(x²-22x+131)(x-11)
[Simplify and divide out the common factor 9.]

= x²-x-100x-11 ÷-[x²-22x+131]x-11
[Take out the common factor.]

= x²-x-100x-11 -(x-11)[x²-22x+131]
[Cancel the common factors.]

= - x²-x-100x²-22x+131
[Divide out the common factor (x - 11).]


Correct answer : (4)
 7.  
Simplify:
-3c+4+4c-2-c-5c+2(c-2)²
a.
4c³+15c²+20cc4+4c³-9c²
b.
4c³-15c²+20c-12-c4+4c³-9c²+22c-20
c.
-15c²+20c-12c4-4c³+9c²-22c+20
d.
None of the above


Solution:

-3c+4+4c-2-c-5c+2(c-2)²

= -3(c-2)+4c(c-2)+4cc(c-2)- c[c(c-2)²]-5(c-2)²+2cc(c-2)²
[Take LCD in the numerator and the denominator.]

= 4c²-7c+6-c4+4c³-9c²+22c-20(c-2)
[Simplify.]

= [4c²-7c+6](c-2)-c4+4c³-9c²+22c-20
[Divide out the common factor c(c - 2).]

= 4c³-15c²+20c-12-c4+4c³-9c²+22c-20
[Multiply with the reciprocal.]


Correct answer : (2)
 8.  
Simplify:
5x+9y-4x+6y
a.
5x+9y- 4y+6x
b.
- 4y+6x5y+9x
c.
5y+9x- 4x+6y
d.
5y+9x-4y+6x


Solution:

5x+9y-4x+6y

= xyxy5x+9y-4x+6y
[The LCD is xy, so multiply by xyxy.]

= xy5x+xy9yxy-4x+xy6y
[Distributive property.]

= 5y+9x-4y+6x


Correct answer : (4)
 9.  
Simplify:
5m(10a-10b)2 +6n(a-b)310l(10a-10b)3
a.
[5ma + 5mb + 600n]l
b.
[ma - mb + 120n]20l
c.
[5ma - 5mb + 600n]l
d.
[ma - mb + 120n]5l


Solution:

5m(10a-10b)2 +6n(a-b)310l(10a-10b)3

= 5m102(a-b)2+6n(a-b)310l103(a-b)3
[Take out the common factor.]

= m20(a-b)2+6n(a-b)3l100(a-b)3
[Cancel the common factors.]

= m(a-b)+120n20(a-b)3l100(a-b)3
[Take LCD in the numerator.]

= ma-mb+120n20(a-b)3l100(a-b)3
[Simplify.]

= ma-mb+120n20(a-b)3÷l100(a-b)3
[Rewrite.]

= ma-mb+120n20(a-b)3100(a-b)3l
[Multiply with the reciprocal.]

= 5ma - 5mb + 600nl
[Cancel the common factors.]


Correct answer : (3)
 10.  
Simplify:
(13c)/(12c)
a.
156c²
b.
13 12
c.
12 13
d.
12c²13


Solution:

(13c)/(12c)

= 13c ÷12c
[Rewrite.]

= 13c c12
[Multiply with the reciprocal.]

= 13 / 12
[Cancel the common factors.]


Correct answer : (2)

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