By simplifying the right-hand side of the equation, show that 1500e^x/(1+e^x)^2= 1/1500(-1500/(1+e^t)+1500)(1500-(-1500/(1+e^x)+1500))

Question

Simplify the right hand side so that it equals to the left hand side.

1500e^x/(1+e^x)^2= 1/1500(-1500/(1+e^t)+1500)(1500-(-1500/(1+e^x)+1500))

Answer 1

Here is your solution,

 

https://ibb.co/jzQ017Q

Answer 2

Correction: eᵗ should be eˣ.

-1500/(1+eˣ)+1500=1500(-1/(1+eˣ)+1)=1500eˣ/(1+eˣ);

1500-(-1500/(1+eˣ)+1500)=1500/(1+eˣ).

The product of these is 1500²eˣ/(1+eˣ)² and the expression on the right becomes:

(1/1500)1500²eˣ/(1+eˣ)²=1500eˣ/(1+eˣ)², QED