Question

Show that 1/1+xa-b + 1/1+Xb-a = 1

Answer 1

Answer:

i hope this answer will help you

Answer 2

$\displaystyle \sf{ \frac{1}{1 + {x}^{a - b} } + \frac{1}{ 1 + {x}^{b - a} } = 1 } \: \: is \: \bf proved$

Given :

$\displaystyle \sf{ \frac{1}{1 + {x}^{a - b} } + \frac{1}{ 1 + {x}^{b - a} } = 1 }$

To find :

To prove the expression

Solution :

Step 1 of 2 :

Write down the given expression to prove

Here the given expression is

$\displaystyle \sf{ \frac{1}{1 + {x}^{a - b} } + \frac{1}{ 1 + {x}^{b - a} } = 1 }$

Step 2 of 2 :

Prove the expression

$\displaystyle \sf{ \frac{1}{1 + {x}^{a - b} } + \frac{1}{ 1 + {x}^{b - a} } }$

$\displaystyle \sf{ = \frac{1}{1 + \frac{ {x}^{b} }{ {x}^{a} } } + \frac{1}{ 1 + \frac{ {x}^{a} }{ {x}^{b} } } }$

$\displaystyle \sf{ = \frac{1}{ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} } } + \frac{1}{ \frac{{x}^{b} + {x}^{a} }{ {x}^{b} } } }$

$\displaystyle \sf{ = \frac{1}{ \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} } } + \frac{1}{ \frac{ {x}^{a} + {x}^{b} }{ {x}^{b} } } }$

$\displaystyle \sf{ = \frac{ {x}^{a} }{ {x}^{a} + {x}^{b} } + \frac{ {x}^{b} }{ {x}^{a} + {x}^{b} } }$

$\displaystyle \sf{ = \frac{ {x}^{a} + {x}^{b} }{ {x}^{a} + {x}^{b} } }$

$\displaystyle \sf{ = 1}$

Hence the proof follows

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ find the value of x (2) 5) -³×(2/5) ^18=(2/5)^10x

https://brainly.in/question/47348923

2. If (-2)m+1 × (-2)4 = (-2)6 then value of m =

https://brainly.in/question/25449835