Umformen (wie muss ich das machen)

Question

Hallo,

ich muss nach w umformen,wie geht das?

c= \( \frac{4+w}{w+3} \)

  :)

Answer 1

\(\begin{aligned} c & =\frac{4+w}{w+3} &  & |\cdot\left(w+3\right)\\ c\cdot\left(w+3\right) & =4+w\\ cw+3c & =4+w &  & |-w\\ \left(c-1\right)w+3c & =4 &  & |-3c\\ \left(c-1\right)w & =4-3c &  & |:\left(c-1\right)\\ w & =\frac{4-3c}{c-1} \end{aligned}\)

Answer 2

Aloha :)$$\left.c=\frac{4+w}{w+3}=\frac{w+\overbrace{3+1}^{=4}}{w+3}=\frac{w+3}{w+3}+\frac{1}{w+3}=1+\frac{1}{w+3}\quad\right|\;-1$$$$\left.c-1=\frac{1}{w+3}\quad\right|\;\text{Kehrwert}$$$$\left.\frac{1}{c-1}=w+3\quad\right|\;-3$$$$w=\frac{1}{c-1}-3$$