Question:
If
\[
\frac{2x+5}{(x-1)(x+3)}
=
\frac{A}{x-1}+\frac{B}{x+3},
\]
then \(A+B=\)
If
\[
\frac{2x+5}{(x-1)(x+3)}
=
\frac{A}{x-1}+\frac{B}{x+3},
\]
then \(A+B=\)
Show Hint
In partial fractions, after taking LCM, compare coefficients of like powers of \(x\).
Updated On: May 27, 2026
- \(-2\)
- \(2\)
- \(1\)
- \(-1\)
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The Correct Option is B
Solution and Explanation
Concept:
This is a partial fraction problem. We compare coefficients after taking common denominator.
Step 1: Given: \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1}+\frac{B}{x+3} \]
Step 2: Take LCM on the right side: \[ \frac{A}{x-1}+\frac{B}{x+3} = \frac{A(x+3)+B(x-1)}{(x-1)(x+3)} \]
Step 3: Since denominators are same, compare numerators: \[ 2x+5=A(x+3)+B(x-1) \]
Step 4: Expand: \[ 2x+5=Ax+3A+Bx-B \] \[ 2x+5=(A+B)x+(3A-B) \]
Step 5: Compare coefficient of \(x\): \[ A+B=2 \] \[ \boxed{2} \]
This is a partial fraction problem. We compare coefficients after taking common denominator.
Step 1: Given: \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1}+\frac{B}{x+3} \]
Step 2: Take LCM on the right side: \[ \frac{A}{x-1}+\frac{B}{x+3} = \frac{A(x+3)+B(x-1)}{(x-1)(x+3)} \]
Step 3: Since denominators are same, compare numerators: \[ 2x+5=A(x+3)+B(x-1) \]
Step 4: Expand: \[ 2x+5=Ax+3A+Bx-B \] \[ 2x+5=(A+B)x+(3A-B) \]
Step 5: Compare coefficient of \(x\): \[ A+B=2 \] \[ \boxed{2} \]
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