\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / A1 Algebraic Techniques / E7 Solving Multivariable Equation

Solve the equation for \(w\):

\[ \frac{3w+4}{{s}}=\frac{3w-4}{{s}}+\frac{s-1}{{w}} \]

Solution: \[\begin{{array}}{{rcl}} \frac{3w+4}{{s}}&=&\frac{3w-4}{{s}}+\frac{s-1}{{w}}\\ \frac{(3w+4){\color{{red}} s w}}{{s }}&=&\frac{(3w-4) {\color{{red}} s w}}{{s }}+\frac{(s-1) {\color{{red}} s w}}{{w}}\\ 3w^2+4w&=&3w^2-4w+s^2-s\\ 8w&=&s^2-s\\ w&=&\frac{s^2-s}{{8}} \end{{array}} \]