SOLUTION: 1/x + 1/xy =x solve for y in terms of x if x (does not equal) 0, and y (does not equal) 0 I keep trying to factor it and come out with a strange answer every time, help woul

Question 1111716: 1/x + 1/xy =x
solve for y in terms of x if x (does not equal) 0, and y (does not equal) 0
I keep trying to factor it and come out with a strange answer every time, help would be much appreciated! Thank you!
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1/x + 1/xy =x
solve for y in terms of x
Multiply thru by xy
y + 1 = x^2y
x^2y - y = 1
y*(x^2-1) = 1
y = 1/(x^2-1)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The answer by the other tutor is exactly right, and probably the easiest way to do it. Let me just expand on his solution so you can see WHY he did what he did; that should help you when you see another problem like this.

1/x + 1/xy =x
solve for y in terms of x
(1) Multiply thru by xy:
y + 1 = x^2y

You can probably work the problem without doing that; but clearing the denominators will make the work MUCH easier.

(2) Gather all the terms containing y, and only those terms, on one side of the equation:
x^2y - y = 1

That step is required....

(3) Factor out the "y" from each term:
y*(x^2-1) = 1

This step is also required. Note that this will only be possible if y only appears in each term to the 1st power. For example, if at this point your equation is x^2y - y^2 = 1, you won't be able to solve the original equation for y.

(4) Divide both sides of the equation by the other factor, leaving y by itself -- giving you the final answer.
y = 1/(x^2-1)
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