# Thread: Can someone help me solve this equation?

1. ## Can someone help me solve this equation?

Equation: x = ( y+z ) / ( y-z )

We only know x and z, I try to solve:

x ( y-z) = y+z
xy - xz = y + z
xy - y = z + xz

But this method not resolve it.

Can you help me?

Sorry for my english but I am not english

Thanks!

2. ## Re: Can someone help me solve this equation?

$x = \dfrac{y+z}{y-z}$

solving for $y$

$(y-z)x = y+z$

$x y - x z = y + z$

$xy - y = xz + z$

$(x-1)y = x(z+1)$

$y = \dfrac{x(z+1)}{x-1}$

3. ## Re: Can someone help me solve this equation?

Originally Posted by romsek
$x = \dfrac{y+z}{y-z}$

solving for $y$

$(y-z)x = y+z$

$x y - x z = y + z$

$xy - y = xz + z$

$(x-1)y = x(z+1)$

$y = \dfrac{x(z+1)}{x-1}$
I should add that the step

$(x-1)y = x(z+1) \to y = \dfrac{x(z+1)}{x-1}$

is valid only if $x \neq 1$

4. ## Re: Can someone help me solve this equation?

Originally Posted by romsek
$xy - y = xz + z$

$(x-1)y = x(z+1)$
Typo: = z(x+1)
To the corner for (x + z) minutes...