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

17. given equation is   (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 2

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)

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

above  eqution cancel

     = -1 / 1

     = - 1

 the answer is a