Question

How do you express `1/(e^x(e^x+1))` in partial fractions?

Answer 1

`1/(e^x(e^x+1)) = 1/e^x-1/(e^x+1)`

Explanation:

Making `1/(e^x(e^x+1)) = A/e^x+B/(e^x+1)` after equating numerator coefficients we have

`{ (A+B=0), (A=1) :}`

Solving for `A,B` we obtain

`1/(e^x(e^x+1)) = 1/e^x-1/(e^x+1)`