y+2/y =1/y-5
*Please solve the rational equation
I am not certain if the right term is
1/(y-5) or the right side is 1/y -5
To solve the rational equation, we need to find the value(s) of y that satisfy the equation. However, it seems like there might be confusion about the arrangement of the terms in the equation.
If the equation is:
y + 2/y = 1/(y - 5)
We can start by eliminating the fractions by multiplying through by the denominators:
(y)(y - 5)(y + 2/y) = (y)(y - 5)(1/(y - 5))
The goal is to cancel out the denominators, so expanding both sides will help us simplify the equation:
y^2(y - 5) + 2(y - 5) = y(y - 5)(1)
Now, distribute and simplify:
y^3 - 5y^2 + 2y - 10 = y^2 - 5y
Next, let's gather all the terms on one side of the equation and simplify further:
y^3 - 5y^2 + 2y - 10 - y^2 + 5y = 0
Combining like terms:
y^3 - 6y^2 + 7y - 10 = 0
At this point, we have a cubic equation. To find the solutions, we can use various methods like factoring, synthetic division, or numerical methods. Without additional information or clarification of the equation, it's challenging to provide the exact solutions.