Simplify $\frac{\sin(ax)\cosh(bx)+\frac{a}{b}\cos(ax)\sinh(bx)}{\sin(ax)\sinh(bx)+\frac{a}{b}\cos(ax)\cosh(bx)}$

Question

The equation $$\frac{\sin(ax)\cosh(bx)+\frac{a}{b}\cos(ax)\sinh(bx)}{\sin(ax)\sinh(bx)+\frac{a}{b}\cos(ax)\cosh(bx)}$$ appears frequently in quantum mechanics to represent the time delays incurred from reflecting off of an infinite barrier adjacent to a potential well. Is there any means to simplify it? I considered trying to expand the formula in terms of complex exponentials or special functions, but I was largely unsuccessful. I also tried writing the numerator as a derivative of a function using the product rule, but that only complicated matters further.