How do you multiply #2y + 3 / y = 3/2#?

1 Answer
Jun 21, 2015

Answer:

  • Equation obtained after multiplying:
    #color(red)(4y^2 - 3 y+6=0#
  • The solution:
    #color(red)( (3+-sqrt(-87))/8#

Explanation:

#2y + 3 / y = 3/2#
Taking L.C.M on the L.H.S

#(2y^2 + 3) / y =color(green)( 3/2#

Cross multiplying

#(2y^2 + 3) . color(green)(2 )= 3 . color(green)(y#
#4y^2 + 6= 3 y#
#color(red)(4y^2 - 3 y+6=0#

solving the equation :
The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-3)^2-(4*(4)*6)#

# = 9-96=-87#
As, #Delta<0# there are complex solutions

The solutions are found using the formula
#x=(-b+-sqrtDelta)/(2*a)#

As #Delta = -87#, #x = (-(-3)+-sqrt(-87))/(2*4) =color(red)( (3+-sqrt(-87))/8#