If $\tan \theta = \frac{a}{b}$, find the value of $\frac{a\sin \theta - b\cos \theta}{a\sin \theta + b\cos \theta}$.

Options:

• A: $\frac{a^2 + b^2}{a^2 - b^2}$
• B: $\frac{a^2 - b^2}{a^2 + b^2}$
• C: $\frac{a - b}{a + b}$
• D: $\frac{a + b}{a - b}$

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