Linear Equations| Algebra| ENGG10 LE3| Problem 2

Solve for y in terms of the other symbols

\frac{1}{c-y}+\frac{2}{c+y}=\frac{1}{y}

SOLUTION:

Multiply both sides by the LCD \left(c-y\right)\left(c+y\right)\left(y\right)

y\left(c+y\right)+2y\left(c-y\right)=\left(c+y\right)\left(c-y\right)

cy+y^2+2cy-2y^2=c^2-y^2

\left(y^2-2y^2+y^2\right)+\left(cy+2cy\right)=c^2

0+3cy=c^2

3cy=c^2

y=\frac{c^2}{3c}

y=\frac{c}{3}