Question

42/63 = k/k-2 stuck on this problem

Answer 1

What are you being asked to do here? Solve for "\(\sf \color{blue}{k}\)" ?
\(\large \sf \frac{42}{63} = \frac{k}{k-2}\)

Answer 2

First, simplify the left hand side, which is approximately 0.667, so you have \(\large \sf 0.667 = \frac{k}{k-2}\), now multiply both sides by \(\sf \color{red}{k-2}\), this eliminates the k-2 on the right hand side, to give you: \(\large \sf 0.667(k-2) = k\), next distrbute inside the parenthesis: \(\sf \color{blue}{0.667k - 1.334 = k}\)
Now, combine like terms, substract \(\sf \color{red}{0.667k} \) from both sides: \(\sf \color{blue}{ -1.334 = k-0.667k} \Rightarrow \color{green}{0.333k}\) and you have now: \(\sf \color{blue}{-1.334 = 0.333k}\), now divide both sides by 0.333, and \(\sf \color{blue}{k \approx -4}\)

You can also solve as a proportion:
\(\large \sf \frac{42}{63} = \frac{k}{k-2} \Rightarrow \color{red}{42(k-2)=63k}\) then distribute \(\sf \color{red}{42k-84=63k} \Rightarrow \color{orange}{63k-42k =- 84} \Rightarrow \color{blue}{21k=-84}\) your final answer is \(\sf \color{violet}{\frac{-84}{21}} = -4\)