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

Question

Hazel Anglin · Accepted Answer

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

#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#

Genesis Allen · Answer

undefined To multiply the expression (2y + 3) / y by 3/2, you can follow these steps:

1. Simplify the expression (2y + 3) / y by dividing each term by y:
   (2y / y) + (3 / y) = 2 + (3 / y)

2. Multiply the simplified expression by 3/2:
   (2 + (3 / y)) * (3/2)

3. Distribute the multiplication to each term inside the parentheses:
   (2 * (3/2)) + ((3 / y) * (3/2))

4. Simplify the multiplication:
   (6/2) + (9 / (2y))

5. Further simplify:
   3 + (9 / (2y))

Therefore, the multiplication of (2y + 3) / y by 3/2 is 3 + (9 / (2y)).