Question

If \( \frac{6x^3 + 7x^2 - 14x + 11}{6x^3 + x^2 - 10x + 3} = \frac{a}{x + p} + \frac{b}{qx + 3} + \frac{c}{3x + p} \), then \( a + b \) is:

• A. 2
• B. 3
• C. \( \frac{-2}{5} \)
• D. \( \frac{2}{3} \)

Hint:

When dealing with rational expressions, perform polynomial division to break down the given equation and find the required terms.

Answer 1

The Correct Option is A

We are given the rational expression \( \frac{6x^3 + 7x^2 - 14x + 11}{6x^3 + x^2 - 10x + 3} \), and we are asked to find \( a + b \). Step 1: Perform polynomial division on \( \frac{6x^3 + 7x^2 - 14x + 11}{6x^3 + x^2 - 10x + 3} \). Step 2: After dividing, we obtain the required terms for \( a \), \( b \), and \( c \). Step 3: Simplify the values of \( a \), \( b \), and \( c \) and find that \( a + b = 2 \). Thus, the correct answer is 2.