Question

solve the equation : 2(2x -1/x+3) - 3( x+3/2x-1)=5 for x not equal to -3,1/2

Answer 1

let 2x-1/x+3 = Y ----------( 1 )
substitute ( 1 ) in given equation
now,2y-3/y=5
$2y {}^{2} - 3 = 5y \\ 2y {}^{2} - 5y - 3 = 0$
${2y}^{2} - 6y + y - 3 = 0 \\ 2y(y - 3) + 1(y - 3)$
2y+1=0,y-3=0
y=-1/2,y=3
substitute y in ( 1 )
x=-10,-2/5