Who is right about the solutions of this?

Question

Three students were having a disagreement about the number of solutions there are to the rational equation above. Kaitlyn claims that the equation has only one solution, Megan claims the equation has two solutions, and Jon insists the equation has no solution at all! Their teacher told the students that one of them is correct. Which student is right? Prove It! EQUATION: written in words since it will be all over the text box:

x - 4x / (over) x+1 = 4 / (over) x+1

Answer 1

if it x - 4x/(x+1) = 4/(x+1)
then x(x+1) - 4x = 4
or x^2-3x + 4 = 0

this is quadratic and so 2 solutions so Megan is right

you do not have tro evaluate

Answer 2

(x-4x)/(x+1)=4/(x+1)
x is not equal to -1, because at x = -1, the equation is undefined
x-4x=4
-3x=4
x=-4/3
now, you decide who got the right answer,^^
huhmm!!!, i looked back your equation, maybe your equation like this: x -(4x/(x+1))=4/(x+1)
if it is like above, it is different:
x -(4x/(x+1))=4/(x+1)
x(x+1)/(x+1)-4x/(x+1)=4/(x+1)
x cannot equal to -1 like the equation above
x(x+1)-4x=4
x(x+1)-4x-4=0
x^2+x-4x-4=0
x^2-3x-4=0
(x-4)(x+1)=0
x=4, or x=-1, but x canot be -1, so x=4, 1 solution

Answer 3

(x-4x)/(x+1)=4/(x+1)

x-4x=4
-3x=4
x=-3/4 Kaitlyn is right

Answer 4

(x - 4x) / (x+1) = 4 / (x+1)
(-3x / (x+1)) - (4 / (x+1)) = 0
(-3x - 4) / (x+1) = 0

- 3x - 4 = 0
x mustn't be -1 (because you can't divde by 0)

-3x = 4
x = 4/-3

Kaitlyn is right

Answer 5

so I have a question is x-4x divided by x+1 or is just 4x divided by x+1?

Answer 6

(x-4x)/(x+1)=4/(x+1)
x-4x =4
-3x =4
x= -4/3
There is one answer.

Answer 7

only one solution
so Kaitlyn is right