7y-3/y-y^2=1/y-1-5/y(y-1)

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To solve this equation, we first need to combine like terms on both sides of the equation.

Starting with the left side of the equation:
7y - 3/y - y^2 = 1/y - 1 - (5/y)(y-1)
Combine like terms on the left side:
(7y^2 - 3 - y^3) = 1/y - 1 - (5y - 5)
(7y^2 - 3 - y^3) = 1/y - 1 - 5y + 5

Now we need to simplify the remaining terms by getting rid of the fractions.

(7y^2 - 3 - y^3) = 1/y - 1 - 5y + 5
Multiply through by y to get rid of the fractions:
y(7y^2 - 3 - y^3) = y(1/y) - y - 5y^2 + 5y

Simplify the equation further:
7y^3 - 3y - y^4 = 1 - y - 5y^2 + 5y

Rearrange the terms to set the equation to 0:
y^4 + 7y^2 - 5y + 3y + 1 - 5 = 0

y^4 + 7y^2 - 2y - 4 = 0

This is the simplified form of the equation. The next step would be to solve for y, which may require factoring or using another method to find the roots of the equation.