Question #ef937

2 Answers
Sep 4, 2017

e^(x-1) + 1

Could also write this as (e^x + e)/e if that is more helpful.

Explanation:

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

Divide the terms outside the bracket (ie subtract indices)

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

Now multiply through the bracket (ie add indices)

= e^(x-1)*1 + e^(x-1)*e^(1-x)

=e^(x-1) + e^0 = e^(x-1) + 1

Sep 4, 2017

e^(x-1)+1.

Explanation:

Assuming that, simplification for the Exression {e^x(1+e^(1-x))}/e

is reqd.

"The Exp.="{e^x(1+e^(1-x))}/e

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

=e^(x-1)*(1+e^(1-x)).............[because, a^m/a^n=a^(m-n)],

=e^(x-1)*1+e^(x-1)*e^(1-x)........[because, l(m+n)=lm+ln],

=e^(x-1)+e^{(x-)+(1-x)}......[because, a^m*a^n=a^(m+n)],

=e^(x-1)+e^0,

:." The Exp.="e^(x-1)+1, because, a^0=1, ane0.