Anyone help me please ( √(x + 1) + √(x - 1) )/( (√(x + 1) - √(x - 1)) ) + ( √(x + 1) - √(x - 1) )/(( √(x + 1) + √(x - 1)) ) ​

Question

Anyone help me please


`( √(x + 1) + √(x - 1) )/( (√(x + 1) - √(x - 1)) ) + ( √(x + 1) - √(x - 1) )/(( √(x + 1) + √(x - 1)) )`
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Answer 1

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Answer 2

`\\ \rm\hookrightarrow (√(x+1)+√(x-1))/(√(x+1)-√(x-1))+(√(x+1)-√(x-1))/(√(x+1)+√(x-1))`

`\sf Let\begin{cases}\sf √(x+1)=a \\ \sf √(x-1)=b\end{cases}`

Now

`\\ \rm\hookrightarrow (a+b)/(a-b)+(a-b)/(a+b)`

`\\ \rm\hookrightarrow \frac{\left\{(a+b)(a+b)\right\}+\left\{(a-b)(a-b)\right\}}{(a+b)(a-b)}`

`\\ \rm\hookrightarrow ((a+b)^2+(a-b)^2)/(a^2-b^2)`

`\\ \rm\hookrightarrow (a^2+2ab+b^2+a^2-2ab+b^2)/(a^2-b^2)`

`\\ \rm\hookrightarrow (2a^2+2b^2)/(a^2-b^2)`

`\\ \rm\hookrightarrow (2(a^2+b^2))/(a^2-b^2)`

Put values

`\\ \rm\hookrightarrow (2\left[(√(x+1))^2+(√(x-1))^2\right])/((√(x+1))^2-(√(x-1))^2)`

`\\ \rm\hookrightarrow (2(x+1)(x-1))/((x+1)(x-1))`

• Take 2 common

`\\ \rm\hookrightarrow 2\left(((x+1)(x-1))/((x+1)(x-1))\right)`

`\\ \rm\hookrightarrow 2(1)`

`\\ \rm\hookrightarrow 2`