Question

If \( \frac{17x - 2}{12x^2 - x - 20} = \frac{A}{ax + 5} + \frac{B}{3x + b} \), then \( a \cdot A + b \cdot B \) is:

• A. 0
• B. 4
• C. 7
• D. 10

Hint:

For partial fractions, equate the numerators and solve the system of equations to find the unknowns.

Answer 1

The Correct Option is B

We are given the equation \( \frac{17x - 2}{12x^2 - x - 20} = \frac{A}{ax + 5} + \frac{B}{3x + b} \). By solving this equation using partial fractions and simplifying, we find that \( a \cdot A + b \cdot B = 4 \).