APFIVE Trace of a Parametric Matrix
Find all real values of $$x$$ satisfying the equation for the trace of $$T(x)$$:
$$\text{trace}(T(x)) = (2*x+1)+\frac{x}{x+2} = 5.$$
Solve for $$x$$.
Consider the matrix function
$$T(x)=\begin{pmatrix} 2*x+1 & \sqrt{x+4} \\ 3 & \frac{x}{x+2} \end{pmatrix}.$$
A
$$x=\frac{-1\pm\sqrt{65}}{4}$$
B
$$x=2$$
C
$$x=\frac{-1-\sqrt{65}}{4}$$
D
$$x=\frac{-1+\sqrt{65}}{4}$$
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