Not getting how to simplify it

[Amineen]

hi..how can i simplify this..i tried on mathematica but i am getting nothing but the same expression\noindent\(\pmb{-e^{-x} \left(1-e^{-x}\right)^{-1+\beta } \left(1-\left(1-e^{-x}\right)^{\beta }\right)^{-1+\text{$\alpha $1}+\text{$\alpha $2}}

\left(-1+\left(1-\left(1-e^{-x}\right)^{\beta }\right)^{\text{$\alpha $3}}\right) (\text{$\alpha $1}+\text{$\alpha $2}) \beta +}\\

\pmb{\frac{\left(1-e^{-x}\right)^{\beta } \left(1-\left(1-e^{-x}\right)^{\beta }\right)^{-1+\text{$\alpha $1}+\text{$\alpha $3}} \left(\text{$\alpha

$1}+\text{$\alpha $3}-\left(1-\left(1-e^{-x}\right)^{\beta }\right)^{\text{$\alpha $2}} \text{$\alpha $3}\right) \beta }{-1+e^x}}\)

(mentor note: tried to fix this but it didn't look right)

 

[Mark44]

hi..how can i simplify this..i tried on mathematica but i am getting nothing but the same expression

\noindent\(\pmb{-e^{-x} \left(1-e^{-x}\right)^{-1+\beta } \left(1-\left(1-e^{-x}\right)^{\beta }\right)^{-1+\text{$\alpha $1}+\text{$\alpha $2}}

\left(-1+\left(1-\left(1-e^{-x}\right)^{\beta }\right)^{\text{$\alpha $3}}\right) (\text{$\alpha $1}+\text{$\alpha $2}) \beta +}\\

\pmb{\frac{\left(1-e^{-x}\right)^{\beta } \left(1-\left(1-e^{-x}\right)^{\beta }\right)^{-1+\text{$\alpha $1}+\text{$\alpha $3}} \left(\text{$\alpha

$1}+\text{$\alpha $3}-\left(1-\left(1-e^{-x}\right)^{\beta }\right)^{\text{$\alpha $2}} \text{$\alpha $3}\right) \beta }{-1+e^x}}\)

What you wrote is unreadable.

 

[Amineen]

[-e^{-x} (1 - e^-x)^{(-1 + β)} (1 - (1 - e^-x)^\β)^{(-1 + α1 + α2)}(-1 + (1 - (1 - e^-x)^β)^
{α3}) (α1 + α2) β ]+[ ((1 - e^-x)^β (1 - (1 - e^-x)^β)^{(-1 + α1 + α3)} (α1 + α3 - (1 - (1 - e^-x)^β)^{α2 }α3) β)]/ (-1 + e^x)

 

[Mark44]

You don't show how this expression arose, so it's possible that you made an error somewhere along the way. If that's the case, it's futile to try to simplify something that starts off incorrect.

 

[mathman]

[-e^{-x} (1 - e^-x)^{(-1 + β)} (1 - (1 - e^-x)^\β)^{(-1 + α1 + α2)}(-1 + (1 - (1 - e^-x)^β)^
{α3}) (α1 + α2) β ]+[ ((1 - e^-x)^β (1 - (1 - e^-x)^β)^{(-1 + α1 + α3)} (α1 + α3 - (1 - (1 - e^-x)^β)^{α2 }α3) β)]/ (-1 + e^x)

Proofread it. Use $to make it readable. e^-x should be e^{-x}. ^\β is incorrect.$

 

[Amineen]

{-e^{-x} (1 - e^-x)^{(-1 + β)} (1 - (1 - e^{-x})^{β})^{(-1 + α1 + α2)}(-1 + (1 - (1 - e^{-x})^{β})^ {α3}) (α1 + α2) }+{(1 - e^{-x})^{β} (1 - (1 - e^{-x})^{β})^{(-1 + α1 + α3)} (α1 + α3 - (1 - (1 - e^-{x})^{β})^{α2 }α3) β)}/ (-1 + e^{x})
Reference https://www.physicsforums.com/threads/not-getting-how-to-simplify-it.861153/

 

[Mark44]

{-e^{-x} (1 - e^-x)^{(-1 + β)} (1 - (1 - e^{-x})^{β})^{(-1 + α1 + α2)}(-1 + (1 - (1 - e^{-x})^{β})^ {α3}) (α1 + α2) }+{(1 - e^{-x})^{β} (1 - (1 - e^{-x})^{β})^{(-1 + α1 + α3)} (α1 + α3 - (1 - (1 - e^-{x})^{β})^{α2 }α3) β)}/ (-1 + e^{x})
Reference https://www.physicsforums.com/threads/not-getting-how-to-simplify-it.861153/

This is onlyl a slight improvement over what you've already written. Also, the link you added is to this very same thread.
As I already said,

You don't show how this expression arose, so it's possible that you made an error somewhere along the way. If that's the case, it's futile to try to simplify something that starts off incorrect.

You need to show us where the expression above came from. Otherwise I'm going to close this thread.