How to express (1/x+a)*exp(x) in cvx?

a is a constant. x is a scalar and x>0.
I try to divide it into a * exp(x) + exp(x) / x.
And for the second part exp(x)/x, I express it as:
z * inv_pos(x)
(x,1,z) == exponential(1)

however, cvx shows that:
Disciplined convex programming error:
Cannot perform the operation: {real affine} .* {convex}

Could you plz tell me how to express it? Thanks.

t\geq e^x/x, for x>0 is equivalent to t\geq z^2/x followed by z\geq e^{x/2}. The first one is quad_over_lin.

Alternatively, it is also equivalent to x\leq \log{x}+\log{t} which should work out of the box since log is concave.