simplify the expression

Question

5xy/2yz X 4x2y/10y2

a. x3y2/y3z
b. x2y/y2z
c. x2/yz
d. x3/yz

11. simplify
x2-5x-24/6x+2x2 X 5x2/8-x

a. -5x/2
b. 5x2/2x
c. -5x2/2x
d. 5x/2

14. Simplify
x2-y2/2x divided by x-y/6x

a. 3
b. 3x
c. 3(x-y)
d. 3(x+y)

15. Simplify
x2+7x/3x divided by 49-x2/3x-21

a. -1
b. 1
c. x-7/7-x
d. (x+7)(x-7)/(7-x)(7+x)

16. Simplify
6/x2+4x+4 + 5/x+2

a. 11x+12/(x+2)2
b. 11x+22/(x+2)2
c. 5x+8/(x+2)2
d. 5x+16/(x+2)2

17. Simplify
2-5x/x-9+4x-5/9-x

a. -1x+7/x-9
b. -1x-3/x-9
c. -9x+7/x-9
d. 9x2-88x+63/(9-x)(x-9)

18. Simplify
7x/x2-y2 - 1/x-y

a. 6x-y/(x-y)(x+y)
b. 6x+y/(x-y)(x+y)
c. 8x-y/(x-y)(x+y)
d. 8x+y/(x-y)(x+y)

19. Simplify
x+12/4x-16 - x+4/2x-8

a. -1/4
b. -x+10/4(x-4)
c. -x+4/4(x-4)
d. -x+16/4(x-4)

Answer 1

Given 5xy/2yz X 4x2y/10y2

(5xy/2yz)X(4x^2y/10y^2) =

Each ys int the first term cancel each other

(5x/2z)X(4x^2y/10y^2) =

The y in the numerator in the second term.

(5x/2z)X(4x^2/10y) =

Simplify

(5xX4x^2)/(2zX10y) =

(20x^3)/(20zy) =

x^3 / zy

The correct option is D

Answer 2

14. Simplify
x2-y2/2x divided by x-y/6x

Given x2-y2/2x divided by x-y/6x

=> ( x2-y2/2x )/ (x-y/6x)                           ( (a / b) / (c/d) = a / b *d / c)

=> x2 - y2 / 2x *6x / x-y                            (  x2-y2=(x+y) (x-y)  ) 

=> (x - y)  (x + y)  / 2x * 6x / (x-y)             (6x / 2x = 3 ;    (x - y)  (x + y)  / (x-y)   = (x+y))

=> 3*(x+y))

The correct option is D

Answer 3

16.6/x2+4x+4 + 5/x+2

Given 6 / x2+4x+4  +  5 / x+2

The LCM of (x2+4x+4) ,(x+2) is (x2+4x+4)*(x+2)

=>  6 * (x+2)  + 5 (x2+4x+4) /  (x2+4x+4)*(x+2)                         ( (x2+4x+4) = (x+2) ^2  )

=>    6 * (x+2)  + 5(x+2) ^2 /  (x+2) ^2 (x+2)

=>  (x+2) ( 6 + 5 (x+2) /  (x+2)^2 (x+2))                                                    (  (x+2) / (x+2)  = 1 )

=>  6+ 5(x+2)  / (x+2)^2

=> 6 + 5x +10 / (x+2)^2

=> 5x + 16 / (x+2)^2

The best option is D

Answer 4

17.  (2-5x)/(x-9) + (4x-5)/(9-x)

      (2 - 5x)/(x - 9) + (4x - 5)/ -(x - 9)

      (2 - 5x)/(x - 9) - (4x - 5)/(x - 9)

      Here LCM is (x - 9)

      (2 - 5x - (4x - 5))/(x - 9)

      (2 - 5x - 4x + 5)/(x - 9)

      (-9x +7 )/ (x - 9)

     The simplified answer is (-9x +7 )/ (x - 9)

     Here c is the correct answer

Answer 5

18.  (7x)/(x2-y2) - 1/(x-y)

       (7x)/(x-y)(x+y) - 1/(x-y)

       Here LCM of (x-y)(x+y), (x-y) is (x-y)(x+y)

       (7x - 1(x+y))/(x-y)(x+y)

       (7x -x -y)/(x-y)(x+y)

       (6x - y)/(x-y)(x+y)

      The simplified answer is (6x - y)/(x-y)(x+y)

      Here a is the correct answer

Answer 6

16.6/x2+4x+4 + 5/x+2

Given 6 / x2+4x+4  +  5 / x+2

The LCM of (x2+4x+4) ,(x+2) is (x2+4x+4)*(x+2)

=>  6  + 5 (x+2) /  (x2+4x+4)

=> 6 + 5x +10 / (x2+4x+4)

=> 5x + 16 / (x+2)^2

The option  D is best choice

 

Answer 7

19. (x + 12)/(4x -16) - (x + 4)/(2x - 8)

     = (x + 12)/4(x - 4) - (x + 4)/2(x - 4)

     Here LCM of 4(x - 4), 2(x - 4) is 4(x - 4)

     = (x + 12 -2(x + 4)/4(x - 4)

     = ( x + 12 - 2x - 8)/4(x - 4)

     = ( -x + 4 )/4(x - 4)

    The simplified answer is ( -x + 4 )/4(x - 4)

    Here c is the correct answer

Answer 8

15.      (x^2 + 7x)/3x ÷ (49 - x^2)/(3x - 21)

        = (x^2 + 7x)/3x × (3x - 21)/(49 - x^2)

         Rewrite (x^2 + 7x) as x (x + 7), (3x - 21) as 3(x - 7) and (49 - x^2) as (7 - x)(7 + x)

        = x(x + 7)/3x  × 3(x - 7)/(7 - x)(7 + x)

        = (3x)(x + 7)(x - 7)/(3x)(7 - x)(7 + x)

         Cancel common terms

        = (x - 7)/(7 - x)

        The simplified answer is (x - 7)/(7 - x)

         Here c is the answer.

Answer 9

11. (x^2 - 5x - 24)/(6x+2x^2) X (5x^2)/(8 - x)

     = Rewrite x^2 - 5x - 24 as (x + 3) (x - 8) and (6x+2x^2) as 2x(3 + x)

     = (x + 3) (x - 8)/2x(3 + x) X (5x^2)/-(x - 8)

     = (x + 3) (x - 8) (5x^2)/ 2x(3 + x) -(x - 8)

     Cancel common terms

     = (5x^2)/-2x

     = -5x/2

     The simplified answer is -5x/2

     Here a is the correct answer

Answer 10

16.6/x2+4x+4 + 5/x+2

Given 6 / x2+4x+4  +  5 / x+2

The LCM of (x2+4x+4) ,(x+2) is (x2+4x+4)

=6+ 5(x+2)  / (x+2)^2               (x2+4x+4)  factor is (x+2)^2

=(6 + 5x + 10)/ (x+2)^2

=5x + 16 / (x+2)^2

The best option is D