solve this hard equation?

Question

y/m + (y-1)/n = (y-2)/mn

solve for y

Thanks if you can help

Answer 1

Hello

Multiply every term on both sides by the common denominator mn giving us

ny +m(y-1) = y-2

so we have

ny + my -m = y-2 put all the y's on the left and the m on the right giving us

ny +my -y = m -2

factor out y and we have

(n+m-1)y = m-2

divide by (n+m-1) so we get

y = (m-2)/(n+m-1)


Hope This Helps!!

Answer 2

y = (m-2) / (m+n -1)

Answer 3

multiply both sides by mn to get
yn + (y-1)m = y-2
subtract y from both sides
yn + ym -m -y =-2
collect all the y terms together
ym + yn -y =m - 2
factor y out of the polynomial
y(m + n - 1) = m - 2
divide both sides by the polynomial cofactor of y
y = (m - 2)/(m + n -1)

Answer 4

y/m + (y-1)/n = (y-2)/mn

multiply both sides by mn

ny + m(y-1) = y - 2
ny + my - m = y - 2

put y into one side and all others into the other side
by adding m - y to both sides

ny + my -m + m - y = y - 2 + m - y
ny + my - y = m - 2

factor y

(n + m - 1)y = m - 2

divide both sides by (n + m - 1)

y = (m - 2)/(n + m - 1)

Answer 5

y/m + y-1/n =y-2/mn
yn + (y-1)m =y-2 taking LCM
yn +ym -m = y-2
yn +ym -y =m - 2
y(n+m -1) =m-2
y =m-2/n+m-1

Answer 6

y/m + (y-1)/n = (y-2)/mn
yn/mn + m(y-1)/mn = (y-2)/mn
yn + m(y-1) = y-2
ny + my - m = y-2
ny + my - m - y +2 = 0
y(n+m-1) - m + 2 = 0
y(n+m-1) = m - 2
y = (m-2)/(m+n-1)