Question

Use the equation e^x+e^-x/e^x-e^-x=t tosolve for x

Answer 1

Answer:

Step-by-step explanation:

I assume that the equation is

$e^x+\frac{e^{-x}}{e^x} -e^{-x}=t$

$e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t$

$e^{3x}+1-e^x=e^{2x}t$

$e^{3x}-te^{2x}-e^x=-1$

Let u = e^x

$u^3-tu^2-u=-1$

$u(u^2-tu-1) = -1$

if u=1, then $u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0$

then u = 0 (reject) or u = t

So far, we have u = 1 and u = t

if u =1, e^x =1 , then x = 0

if u = t, then e^x = t or x = lnt

Answer 2

Answer:

Solve the rational equation by combining expressions and isolating the variable  

x = ln ( t − √ t ^2 + 4  )/2

x = ln ( t +√ t ^2 + 4  )/2