Find all real values of $$x$$ for which the matrix
$$B=\begin{pmatrix} x & \sqrt{x+5} \\ \frac{2}{x+1} & x-1 \end{pmatrix}$$
is noninvertible (i.e. when $$\det(B)=0$$).
The determinant is given by
$$\det(B)= x*(x-1)-\sqrt{x+5}\cdot\frac{2}{x+1}=0.$$
After clearing denominators and squaring to remove the radical, a higher–degree equation results. The unique solution in the appropriate domain is approximately:

Consider the matrix
$$B=\begin{pmatrix} x & \sqrt{x+5} \\ \frac{2}{x+1} & x-1 \end{pmatrix}.$$
Set \(\det(B)=0\) to determine noninvertibility.