Question

If (2 x- x+λ)/( x+ x-2)dx = A| x+ x-2|+Bx+C, then the ordered triplet (A,B,λ) is

• A. (\frac12,\frac32,-1)
• B. (\frac32,\frac12,-1)
• C. (\frac12,-1,\frac32)
• D. (\frac32,-1,\frac12)

Hint:

Try expressing numerator as derivative of denominator.

Answer 1

The Correct Option is B

Let denominator D= x+ x-2. Match numerator with derivative of denominator: D'=- x+ x Comparing coefficients gives: A=\frac32, B=\frac12, λ=-1