[Crimson Dynamo]

First, tan x = 3/4 ==> sin x = 3/5 by using sohcahtoa and the 3-4-5 right triangle.

Next, sin(pi - x) = sin pi cos x - cos pi sin x = sin x.
Since tangent has period pi, tan(pi+x) = tan(4pi+x) = tan x.

Next,
cos(3pi/2+x) = cos(3pi/2) cos x - sin(3pi/2) sin x = sin x
cos(5pi/2-x) = cos(5pi/2) cos x + sin(5pi/2) sin x = sin x

So,
(sin(pi - x) + tan(pi+x) + tan(4pi+x)) /(cos(3pi/2+x)+cos(5pi/2-x))
= (sin x + tan x + tan x) / (sin x + sin x)
= (sin x + 2 tan x)/ (2 sin x).
= (3/5 + 2 * 3/4)/ (2 * 3/5)
= 7/4.