Could anyone help step me through solving these three equations, I get lost in massive fractions and squares etc:

$$ \begin{align}\frac{\frac{yz}{y+z}}{x + \frac{yz}{y+z}} &= \frac{1}{2} \tag{1} \\ \frac{\frac{xz}{x+z}}{y + \frac{xz}{x+z}} &= \frac{1}{6} \tag{2} \\z &= 10 \tag{3} \end{align} $$

  • $\begingroup$ First simplify fractions like $\frac{yz}{y}=z$ with a reminder that $y\ne 0$. Then substitute $z=10$ in the other two equations. Then, if you still get stuck along the way, edit your question and post the progress, then point at where in particular you got stuck. $\endgroup$ – dxiv May 9 '17 at 6:45
  • $\begingroup$ Hi @dxiv, thanks, someone else edited my post and it changed the question. I've edited it back so you'll see yz/y = z situations don't exist. $\endgroup$ – edd91 May 9 '17 at 6:50
  • $\begingroup$ That's one more good reason for you to use MathJax when posting. That said, the second part of my previous comment still applies. $\endgroup$ – dxiv May 9 '17 at 6:54

The first equation can be written as


The second equation can be written as


So we have





So $y=20$.


$\displaystyle x=\frac{20}{3}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.