Question

solve the equation 2(3x-5/x+2)-5(x+2/3x-5)=3 where x≠-2and x≠5/3​

Answer 1

hope this helps

thanks for asking

Answer 2

Given :  2 (3x - 5)/(x + 2)  -  5(x + 2)/(3x - 5)  = 3

To Find : Solve for x

Solution:

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

Let  (3x - 5)(x + 2)   = y   => (x + 2)/(3x - 5) = 1/y

=> 2y  - 5/y  = 3

=> 2y²  - 5 = 3y

=> 2y²  - 3y  - 5 = 0

=> 2y²  - 5y  + 2y  - 5 = 0

=> 2y(y + 1) - 5(y + 1)  = 0

=> y = - 1   or y  = 5/2

(3x - 5)(x + 2)   = - 1

=> 3x - 5  = - x - 2

=> 4x  = 3

=> x = 3/4

(3x - 5)(x + 2)   =  5/2

=> 6x - 10 =  5x + 10

=> x = 20

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