TS EAMCET · Maths · Basic of Mathematics
If \(\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{\mathrm{A} x+\mathrm{B}}{x^2+2}+\frac{\mathrm{C} x+\mathrm{D}}{x^2+3}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)
- A 0
- B 1
- C -1
- D 6
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
Let \( y=x^2 \). \( \frac{y+1}{\left(y+2\right)\left(y+3\right)}=\frac{\mathrm{E}}{y+2}+\frac{\mathrm{F}}{y+3} \) \( y+1 = \mathrm{E}(y+3)+\mathrm{F}(y+2) \) For \( y=-2 \): \( -2+1 = \mathrm{E}(-2+3) \Rightarrow \mathrm{E}=-1 \) For \( y=-3 \):…
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