TS EAMCET · Maths · Basic of Mathematics
If \(\frac{x+1}{x^3(x-1)}=\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3}+\frac{d}{x-1}\) then
- A \(a=b=c=-d\)
- B \(a=b=2 c=-d\)
- C \(a=2 b=c=-d\)
- D \(a=b=2 c=d\)
Answer & Solution
Correct Answer
(B) \(a=b=2 c=-d\)
Step-by-step Solution
Detailed explanation
\(x+1 = a x^2(x-1) + b x(x-1) + c(x-1) + d x^3\) For \(x=0\): \(1 = c(0-1) \implies 1 = -c \implies c = -1\) For \(x=1\): \(2 = d(1)^3 \implies d = 2\) \(x+1 = (a+d)x^3 + (-a+b)x^2 + (-b+c)x - c\) Equating coefficients of \(x^3\): \(0 = a+d \implies 0 = a+2 \implies a = -2\)…
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