Question

Xác định các số a, b biết:

\(\frac{\left(3x+1\right)}{\left(x+1\right)^3}\)=\(\frac{a}{\left(x+1\right)^3}\)+\(\frac{b}{\left(x+1\right)^2}\)

Answer 1

3x + 1 = 3(x+1) -2 Vậy a = -2 ; b = 3

Answer 2

\(\frac{3x+1}{\left(x+1\right)^3}=\frac{a}{\left(x+1\right)^3}+\frac{b}{\left(x+1\right)^2}\Leftrightarrow\frac{3x+1}{\left(x+1\right)^3}=\frac{a}{\left(x+1\right)^3}+\frac{b.\left(x+1\right)}{\left(x+1\right)^3}\)

\(\Rightarrow\frac{3x+1}{\left(x+1\right)^3}-\frac{a+b.\left(x+1\right)}{\left(x+1\right)^3}=0\)\(\Rightarrow3x+1=a+b.\left(x+1\right)\)

Mà 3x+1=3.(x+1) -2  \(\Rightarrow b=3,a=-2\)