Question

MATH - 2(2x+3/x-3)-25(x-3/2x3)=5 (x≠3),(x≠-3/2)​

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

therefore the values of x are 1,6 Answer

Answer 2

Answer : 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 therefore the values of x are 1,6 Answer

Hope it helps ❤️