1/a-y=1/y

solve for "y"

Please change your screenname, it is just a little presumptious that somehow you should go to the head of the line.

is the left side

1/(a-y) or (1/a) - y ?

If it is 1/(a-y) = 1/y

then cross multiply to get y = a -y

solve for y in terms of a.

cross multiply is a very dangerous term for beginning students. Change your thinking to

multipy both sides by y then
multiply both sides by a-y
giving
y=a-y
then add y to both sides
2y=a
divide both sides by 2
y=a/2

three times a number, minus 6,is the same as two times a number, plus 3 find the numb

To solve for "y" in the equation 1/(a - y) = 1/y, we need to manipulate the equation to isolate "y" on one side. Here's how you can do it:

Step 1: Simplify the fractions by finding a common denominator.
- Multiply both sides of the equation by y(a - y) to eliminate the fractions.
- The equation becomes y = y(a - y).

Step 2: Expand the equation.
- Distribute y into the equation: y = ya - y^2.

Step 3: Rearrange the equation to put it in quadratic form.
- Move all terms to one side of the equation: y^2 + y - ya = 0.

Step 4: Factor the equation if possible.
- In this case, the equation can't be easily factored.

Step 5: Solve the equation using the quadratic formula.
- The quadratic formula is given by: y = (-b ± √(b^2 - 4ac)) / (2a).
- For our equation y^2 + y - ya = 0, the coefficients are a = 1, b = 1, and c = -a.
- Substituting these values into the quadratic formula, we have y = (-1 ± √(1 - 4(-a))) / 2.

So the solution for "y" in the equation 1/(a - y) = 1/y is:
y = (-1 ± √(1 + 4a)) / 2.