Please explain how does z=-2? 4/(z^2-z) - 2 = 4/(z-1)

[adevine]

When I solve this, I keep getting z as 1. But I already know that z can't be 1 (or 0). I looked up the answer and saw that it is -2. How does that work? What am I missing?

 

[galactus]

Re: Please explain... how does z=-2?

Your LCD is z(z-1)

\(\displaystyle \frac{4}{z(z-1)}-\frac{z(z-1)}{z(z-1)}\cdot\frac{2}{1}=\frac{z}{z}\cdot\frac{4}{z-1}\)

Now that the denominators are the same, you have:

\(\displaystyle 4-2z(z-1)=4z\)

Solve and you will get two solutions, but only one will satisfy the equation.

 

[adevine]

Re: Please explain... how does z=-2?

Thanks!

 

[Loren]

When Galactus says "Now that the denominators are the same" then uses only the numerators to build the equation, he has essentially multiplied both sides of the equation (all terms) by the common denominator. Try it to see what happens.