If 3 tan θ = 4 for an acute angle θ, find the value of (4 sin θ - cos θ)/(4 sin θ + cos θ).

Step 1. The triangle. Opposite $4k$, adjacent $3k$, hypotenuse $5k$.

Step 2. The ratios. $\sin \theta = \dfrac{4}{5}$ and $\cos \theta = \dfrac{3}{5}$.

Step 3. Substitute. Top: $\dfrac{16}{5} - \dfrac{3}{5} = \dfrac{13}{5}$. Bottom: $\dfrac{16}{5} + \dfrac{3}{5} = \dfrac{19}{5}$.

Step 4. Divide. $\dfrac{13}{5} \div \dfrac{19}{5} = \dfrac{13}{19} \approx 0.684$.