Solve: (2/y+2)+(3/y)=(-y/y+2)
To solve the equation (2/y+2)+(3/y)=(-y/y+2), we need to find the value of 'y' that makes the equation true.
Let's simplify the equation step by step:
First, we need to find a common denominator for all the fractions. In this case, the common denominator is 'y+2'.
Rewriting the equation with the common denominator:
((2(y+2))/((y+2) * y)) + ((3(y+2))/((y+2) * y)) = (-y/(y+2))
Now, we need to combine the fractions on the left side of the equation:
((2(y+2) + 3(y+2))/((y+2) * y)) = (-y/(y+2))
Expanding and simplifying the numerators:
((2y + 4) + (3y + 6))/((y+2) * y) = (-y/(y+2))
Combining like terms:
(5y + 10)/((y+2) * y) = (-y/(y+2))
Next, we can cross-multiply to eliminate the denominators:
(5y + 10) * (y+2) = -y * y
Expanding the left side of the equation:
5y^2 + 20y + 10y + 20 = -y^2
Combining like terms:
5y^2 + 30y + 20 = -y^2
Moving all terms to one side of the equation:
6y^2 + 30y + 20 = 0
Now we have a quadratic equation. We can attempt to factor it or use the quadratic formula to find the possible values of 'y'.