(4-y^2)/(y-2) = y/2
(4-y^2)/(y-2) = y/2
4 - y^2 = (y*(y-2))/2
4 - y^2 = (y^2-2y)/2
8 - 2y^2 = y^2 - 2y
3y^2 - 2y - 8 = 0
(keep the above equation in mind)
quadratic formula:
(-b +/- sqrt(b^2 - 4ac))/2a
now solve by plugging in the appropriate numbers and choose (normally) the positive or higher value.
(4-y^2)/(y-2) = y/2 Factor
(y-2)(y+2)/(Y-2)= y/2
y+2=y/2
y/2=-2
y=-4
Julie made and error in her post. She multiplied both sides by y-2. This automatically excludes y from being 2. In here conclusion to then proceed, you will get y=2 as a solution in the quadratic. It is not valid.
One cannot multiply both sides of an equation by zero and get a valid answer.
To solve the equation (4-y^2)/(y-2) = y/2, we can follow these steps:
1. Find a common denominator for both sides of the equation. In this case, the common denominator is (y-2)(2).
2. Multiply both sides of the equation by this common denominator to eliminate the denominators. This gives us:
2(4-y^2) = (y^2-2y)(y-2)
3. Simplify the equation by multiplying out the terms:
8 - 2y^2 = y^3 - 4y^2 - 2y^2 + 4y
4. Combine like terms on both sides of the equation:
8 - 2y^2 = y^3 - 6y^2 + 4y
5. Move all terms to one side to set the equation equal to zero:
0 = y^3 - 6y^2 + 4y + 2y^2 - 8 + 8
0 = y^3 - 4y^2 + 4y
6. Simplify the equation if possible, or use the quadratic formula to solve for y. In this case, we have a cubic equation that cannot be simplified further.
7. To solve this cubic equation, we can use numerical or graphical methods to find the value(s) of y that satisfy the equation.