rearrangement of basic algebra equation

When P1 and P2 are known, O is found by:

O=(P1*(1-P2))/(P2*(1-P1))

I need to move P2 to the left side of the equation and O to the right side and then solve for P2 when P1 and O are known. It’s been 20+ years since I did this in high school. Any help would be appreciated. Thanks.

A good first step would be to multiply the denominator "up" onto the left-hand side.

Then multiply things out to get rid of the parentheses.

Move all the terms containing P₂ to one side of the equation, and all the other terms to the other side.

Then factor the P₂ out of those terms, and divide off whatever is left.

If you get stuck, please reply showing what you've tried and how far you've gotten.

Thank you.

Eliz.

RayTom said:

O=(P1*(1-P2))/(P2*(1-P1))
I need to move P2 to the left side of the equation.

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Make your life easier by using SIMPLE variables ; O=x, P1=a, P2=b
So this makes your equation:
x = a(1 - b) / (b(1 - a))

crisscross multiplication:
xb(1 - a) = a(1 - b)

do the multiplications:
xb - xba = a - ab

move -ab to left (to have all terms with b together):
xb + ab - xba = a

isolate the b:
b(x + a - xa) = a
so b = a / (x + a - xa)

Thank you for your help. It has actually been 30+ years since I've done algebra.

RayTom said:

Thank you for your help. It has actually been 30+ years since I've done algebra.

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Ray, I went back to algebra 5 years ago, when I retired;
had been away over 40 years: so you get no sympathy from me :wink: