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 \(x\). This quickly gives the required constants.
Updated On: May 7, 2026
- \(-2\)
- \(2\)
- \(1\)
- \(-1\)
Show Solution
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The Correct Option is B
Solution and Explanation
We are given
\[
\frac{2x+5}{(x-1)(x+3)}=\frac{A}{x-1}+\frac{B}{x+3}.
\]
Taking LCM on the right-hand side:
\[
\frac{A}{x-1}+\frac{B}{x+3}
=
\frac{A(x+3)+B(x-1)}{(x-1)(x+3)}.
\]
So,
\[
\frac{2x+5}{(x-1)(x+3)}
=
\frac{A(x+3)+B(x-1)}{(x-1)(x+3)}.
\]
Since denominators are same, numerators must be equal:
\[
2x+5=A(x+3)+B(x-1).
\]
Expand the right-hand side:
\[
2x+5=Ax+3A+Bx-B.
\]
\[
2x+5=(A+B)x+(3A-B).
\]
Now compare coefficients.
Coefficient of \(x\):
\[
A+B=2.
\]
Constant term:
\[
3A-B=5.
\]
The question asks directly for \(A+B\).
Therefore,
\[
A+B=2.
\]
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