6-1-c-x-1-1-c-x-y-Express-11-1-c-x-1-1-c-x-in-terms-of-y-

Question Number 176785 by Ar Brandon last updated on 26/Sep/22

\frac{6}{1 + c^{x}} + \frac{1}{1 + c^{- x}} = y

Express \frac{11}{1 + c^{x}} + \frac{1}{1 + c^{- x}} in terms of y

Commented by Ar Brandon last updated on 26/Sep/22

Ans . 2 y - 1

Answered by a.lgnaoui last updated on 26/Sep/22

y = 6 \frac{1}{1 + c^{x}} + \frac{1}{1 + \frac{1}{c^{x}}} = 6 \frac{1}{1 + c^{x}} + \frac{c^{x}}{1 + c^{x}}

y = 6 \frac{1}{1 + c^{x}} + \frac{1 + c^{x} - 1}{1 + c^{x}} = 5 \frac{1}{1 + c^{x}} + 1

\frac{11}{1 + c^{x}} + \frac{1}{1 + c^{- x}} = \frac{11}{1 + c^{x}} + 1 - \frac{1}{1 + c^{x}} = 10 \frac{1}{1 + c^{x}} + 1

\frac{11}{1 + c^{x}} + \frac{1}{1 + c^{- x}} = 2 y - 1

Commented by Ar Brandon last updated on 26/Sep/22

Thank you, Sir!

Answered by mr W last updated on 26/Sep/22

\frac{6 + c^{x}}{1 + c^{x}} = y

\frac{5}{1 + c^{x}} = y - 1

\frac{11}{1 + c^{x}} + \frac{1}{1 + c^{- x}}

= \frac{6}{1 + c^{x}} + \frac{1}{1 + c^{- x}} + \frac{5}{1 + c^{x}}

= y + y - 1

= 2 y - 1

Commented by Tawa11 last updated on 26/Sep/22

Great sirs

Commented by Ar Brandon last updated on 26/Sep/22

Thank you, Sir!