Okay, I'm in a calculus class but stuck on some algebra...it's not crucial that I get the answer to this but I'm wracking my brain because I can't remember how the following is obtained; if you can show me how this is done in steps I'd greatly appreciate it (I highly suspect it's something simple):
y / (1 - y) = x
solving for y is (I don't know what is being done in between to solve for y):
y = x / (1 + x)
I don't know why I'm having such a hard time with this, thanks for your help in advance.
y / (1 - y) = x
As usual, clear the fraction by multiplying by the denominator:
y = x(1-y)
Now expand to remove parentheses:
y = x - xy
Now collect the y's on one side:
y+xy = x
Factor out the y:
y(1+x) = x
I think you can probably make it from here, no?
Alright I got it thanks so much!!
No problem! Let's go through the steps to solve for y in the equation y / (1 - y) = x.
Step 1: Start by multiplying both sides of the equation by (1 - y) to eliminate the denominator:
y * (1 - y) / (1 - y) = x * (1 - y).
Simplifying the left side of the equation:
y * (1 - y) cancels out the denominator (1 - y), and we are left with:
y = x * (1 - y).
Step 2: Distribute the x on the right side of the equation:
y = x - xy.
Step 3: Move all terms involving y to one side of the equation:
Rearrange the equation to isolate y:
y + xy = x.
Step 4: Factor out y on the left side of the equation:
y(1 + x) = x.
Step 5: Finally, divide both sides of the equation by (1 + x) to solve for y:
y = x / (1 + x).
So, the solution to the equation y / (1 - y) = x, solving for y, is:
y = x / (1 + x).
I hope this step-by-step explanation helps you understand how to solve for y in this algebraic equation! Let me know if you have any further questions.