Question

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

Answer 1

• 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`