Question

Solve for x :
2(2x+3/x-3)-25(x-3/2x+3)=25

Answer 1

 Given : 2( (2x +3)/(x-3))-25(  (x-3)/ (2x +3) )=5
To find : the value of x => 2( (2x +3)/(x-3)) - 25( (x-3)/ (2x +3) )=5
=> [2 (2x +3)2 - 25 (x-3)2 ] / ((x-3) (2x +3)) = 5   {taking LCM}
=> 2 (2x +3)2 - 25 (x-3)2 = 5 (x-3) (2x +3)
=> 2( 4x2 + 9+12x) - 25(x2 + 9 - 6x) = 5(2x2 +3x-6x -9)
=> 8x2 + 18 + 24x -25x2 -225+150x = 10x2 -15x -45
=> -17x2 +174x - 207 = 10x2 -15x -45
=> -27x2 + 189 x -162 =0
=> 27x2 - 189 x + 162 =0
=> x2 -7x +6 =0
=> x2 -6x -x +6 =0
=> x (x-6) -1 (x-6) =0
=> (x-1) (x-6) =0