Question

Solve. z + 6 —- = -7 zSelect the correct answer below, and, if necessary, fill in the answer box within your choice.

Answer 1

`A)z=-1,-6`

1) Let's solve that equation, by taking the LCM (z,1) = z and then dividing by each former denominator and multiplying by its corresponding numerator.

`\begin{gathered} z+(6)/(z)=-7 \\ \frac{\placeholder{⬚}}{z}+\frac{\placeholder{⬚}}{z}=\frac{\placeholder{⬚}}{z} \\ (z^2)/(z)+(6)/(z)=(-7z)/(z) \end{gathered}`

2) Now, we can multiply both sides by z to get rid of those denominators:

`\begin{gathered} z*(z^(2))/(z)+(6)/(z)=(-7z)/(z)* z \\ z^2+6=-7z \\ z^2+7z+6=0 \\ z_=(-7\pm√(7^2-4\cdot\:1\cdot\:6))/(2\cdot\:1) \\ z=-1,z=-6 \end{gathered}`

CaAnd solve the quadratic equation with the formula.