I've got an interesting equation for you. Thank you, very much, for your help if you can show me how it's done

Question

if 1/f =(u-1) ( 1/x -1/y )

express x in terms of the other variables.

Answer 1

OK, first move the u -1: 1/(f(u-1) = 1/x - 1/y

Then move the 1/y: 1/(f(u-1) + 1/y = 1/x

Regroup the left side to get: (y + f(u-1)) / fy(u-1) = 1/x

Finally, invert it (i.e. take the reciprocal) to get:

x = fy(u-1) / (y + f(u-1))

Answer 2

x = { y * f * (u - 1) } / { y - f * (u - 1) }

First convert (1/x - 1/y) to s simple fraction by multiplying 1/x by y/y and 1/y by x/x to get: (x + y) / x*y. Then divide each side by that (or multiply by its inverse) and finally multiply each side by f.

We now have: x*y / (x + y) = f*(u - 1).

Multiply each side by (x + y) to get: x*y = x*f*(u - 1) + y*f*(u - 1) and subtract the "x*f*(u - 1)" term from each side to get the "x's" together: x*y - x*f*(u - 1) = y*f*(u - 1).

Now factor out the "x" terms and divide by the resulting coefficient of "y - f*(u - 1)" to get the answer: x = { y * f * (u - 1) } / { y - f * (u - 1) }.


Sorry to be so prissy with the " *'s " but I decided not to have any reading of the variables read as "f u" just to avoid... um... misunderstandings.

Answer 3

1/f =(u-1) ( 1/x -1/y )
Multiply by fxy to eliminate the fractions:
xy = (u - 1)(fy - fx)
= (u - 1)fy - (u - 1)fx
Add (u - 1)fx to each side:
xy + (u - 1)fx = (u - 1)fy
Factorise out the x:
x(y + (u - 1)f) = (u - 1)fy
Divide by (y + (u - 1)f):
x = (u - 1)fy / (y + (u - 1)f).

Answer 4

1/f =(u-1) ( 1/x -1/y )
1/[f(u-1)] = 1/x - 1/y
1/[f(u-1)] +1/y= 1/x
[y+f(u-1)]/fy(u-1) = 1/x
x = fy(u-1)/[y+f(u-1)]