Find all real solutions Use algebra and show your work 2xx

Find all real solutions. Use algebra and show your work. 2x(x + 3)/(x - 1)(2x -5) = 0 x/3(2x - 1)- 1/4 = 0 x/x - 2 + 1/x - 4 = 2/x^2 - 6x +8

11)

a) 2x(x+3)/(x-1)(2x-5) =0

2x(x+3) =0

x =0 ; x = -3

Solution : x = -3 , 0

b) x/3(2x -1) -1/4 =0

x/3(2x-1) =1/4

4x = 3(2x -1)

4x = 6x -3

-2x = -3 ----> x = 3/2

c) x/(x -2) +1/(x -4) = 2/(x^2 -6x +8)

RHS :2/(x^2 -6x +8) = 2/(x^2 -4x -2x +8) = 2/(x-2)(x-4)

x/(x -2) +1/(x -4) = 2/(x-2)(x-4)

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

cancelling the denominators on both sides:

x^2 -4x +x -2 =2 ----> x^2 -3x -4 =0

x^2 -4x +x -4 =0

x(x -4)+1(x-4) =0

(x+1)(x-4) =0

x = -1 and x=4

Now x =4 is not a solution as at x=4 LHS is undefined

So, only solution x= -1