Question

Explain this please:
(2/(x²+1)(x²+4)) =(2/3)((1/(x²+1))-(1/(x²+4)))

Answer 1

Where you got stucked?

Answer 2

\[\left[ \frac{ 2 }{ (x^{2}+1)(x^{2}+4) } \right] = \frac{ 2 }{ 3 } \left[ \frac{ 1 }{ (x^{2}+1) } - \frac{ 1 }{ (x^{2}+4) } \right]\]

In my textbook they have directly given this answer and I don't know how this has been done. Please explain the steps involved in-between ..

Answer 3

For the denominators with x^2 we'll have to use
\[\frac{2}{(x^2+1)(x^2+4)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+4}\]
Then, multiply by \((x^2+1)(x^2+4)\) both sides
\[2=(Ax+B)(x^2+4)+(Cx+D)(x^2+1)\]

Answer 4

Comparing coefficients
\[x^3: A+C=0 \\ \\ x^2: B+D=0 \\ \\ x:4A+C=0 \\ \\ Constant:4B+D=2\]
Find ABCD

Answer 5

Check if you got \[A=0 \\ \\ B=\frac{2}{3} \\ \\ C=0 \\ \\ D=-\frac{2}{3}\]

Answer 6

Its partial fractions! I never thought of it this way... Thanx Sam!!

Answer 7

Welcome :)