# Problem of the Week

## Updated at May 4, 2020 4:14 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve $$\frac{2(3-z)}{3-{z}^{2}}=2$$?

Check out the solution below!

$\frac{2(3-z)}{3-{z}^{2}}=2$

 1 Multiply both sides by $$3-{z}^{2}$$.$2(3-z)=2(3-{z}^{2})$2 Cancel $$2$$ on both sides.$3-z=3-{z}^{2}$3 Cancel $$3$$ on both sides.$-z=-{z}^{2}$4 Move all terms to one side.$z-{z}^{2}=0$5 Factor out the common term $$z$$.$z(1-z)=0$6 Solve for $$z$$.1 Ask: When will $$z(1-z)$$ equal zero?When $$z=0$$ or $$1-z=0$$2 Solve each of the 2 equations above.$z=0,1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=0,1$Donez=0,1