Final answer:
To make y the subject of the given equation, we can simplify and rearrange the equation. The final expression for y is (a²x + 2ayx - 3√(2x-2x²)(a+2y))/(1-x).
Step-by-step explanation:
To make y the subject of the given equation, we need to isolate y on one side in terms of x. Let's start by simplifying the equation:
ax/(1-x) = 3√(2x) + y/(a+2y)
Multiply both sides by (1-x) to eliminate the denominator:
ax = (1-x)(3√(2x) + y/(a+2y))
Expand the right side:
ax = 3√(2x)(1-x) + y/(a+2y)(1-x)
Simplify the equation further to isolate y:
ax = 3√(2x-2x²) + y(1-x)/(a+2y)
Now, subtract 3√(2x-2x²) from both sides:
ax - 3√(2x-2x²) = y(1-x)/(a+2y)
Multiply both sides by (a+2y) to eliminate the denominator:
(ax - 3√(2x-2x²))(a+2y) = y(1-x)
Expand the left side of the equation:
a(a+2y)x - 3√(2x-2x²)(a+2y) = y(1-x)
Simplify the equation further:
a²x + 2ayx - 3√(2x-2x²)(a+2y) = y - yx
Finally, rearrange the equation to make y the subject:
y = (a²x + 2ayx - 3√(2x-2x²)(a+2y))/(1-x)