Please me in math (a + 1)/(a - 1) + \frac{ {a - 1}^(2) }{a + 1} ​

Question

Please me in math

`(a + 1)/(a - 1) + \frac{ {a - 1}^(2) }{a + 1}`
​

Answer 1

Explanation:

hope this helps you thank you

Answer 2

`\boxed{ \sf{Answer}}`

`\large{\sf(a + 1)/(a - 1) + \frac{ {a - 1}^(2) }{a + 1}}`

Use the algebraic identities ⟶

1. 
   `{\sf(a - b)(a + b) = {a}^(2) - b ^(2)}`
2. 
   `{\sf(a + b) {}^(2) = {a}^(2) + 2ab - {b}^(2)}`
3. 
   `{\sf(a - b) {}^(2) = {a}^(2) - 2ab + {b}^(2)}`

Squaring on both the sides

`{\sf\frac{(a + 1 {)}^(2) + ( {a - 1)}^(2) }{(a - 1)(a + 1)}}`

`=\frac{ {a}^(2) + 2a + 1 + {a}^(2) - 2a + 1 }{ {a}^(2) - 1 } \\ = \frac{ {a}^(2) +\bcancel 2a + 1 + {a}^(2) - \bcancel2a + 1 }{ {a}^(2) - 1 } \\ = \frac{ {a}^(2) + {a}^(2) + 1 + 1 }{ {a}^(2) - 1}`

`\large\boxed{\sf{⟹\frac{ {2a}^(2) + 2}{ {a}^(2) - 1 }}}`

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