Question

What is the answer to 8/z -z=4 in solving rational equations?

Answer 1

Explanation:

8-z^2=4z

8-z^2-4z=0

-z^2-4z+8=0

z^2+4z-8=0

z(z+4)=8

{{z==-5.46410161514},{z==1.46410161514}}

Answer 2

Start with

`(8)/(z)-z=4`

Note that this implies that z cannot be zero, otherwise in the term 8/z you would have a division by zero.

So, supposing that z is not zero, we multiply both sides by z:

`8-z^2=4z`

Rearrange the equation into

`z^2+4z-8=0`

And solve the quadratic equation as usual to get

`z = (-4\pm√(16+32))/(2) = (-4\pm√(48))/(2)= (-4\pm4√(3))/(2) = -2\pm2√(3)`

Since both of these solutions are non-zero, we can accept them.