Question

Helppp!!

Simplify:-
1...a/a-b - b/a+b - 2ab/b²-a²
2...1/a-3 - 1/a-1 + 1/a+3 - 1/a+1
​

Answer 1

#1

`GIVEN;`

`\displaystyle{ (a)/(a - b) - (b)/(a + b) - \frac{2ab}{ {b}^(2) - {a}^(2) } }`

`{ \displaystyle{ (a(a + b) - b(a - b))/((a + b)(a - b)) - \frac{2ab}{ - ( {a}^(2) - {b}^(2) )} } }`

`\displaystyle{ \frac{ {a}^(2) + ab - ab + {b}^(2) }{ {a}^(2) - {b}^(2) } + \frac{2ab}{ {a}^(2) - {b}^(2) } }`

`\displaystyle{ \frac{ {(a + b)}^(2) }{(a + b)(a - b)} }`

`\displaystyle{ \frac{ {(a + b)(a + b)} }{(a + b)(a - b)} }`

`\displaystyle{ (a + b)/(a - b) }`

#2

`GIVEN;`

`\displaystyle{ (1)/(a - 3) - (1)/(a - 1) + (1)/(a + 3) - (1)/(a + 1) }`

`\displaystyle{ (1)/(a - 3) + (1)/(a + 3) - (1)/(a - 1) - (1)/(a + 1) }`

`\displaystyle{ (a + 3 + a - 3)/((a + 3)(a - 3)) - \left( (1)/(a - 1) + (1)/(a + 1) \right) }`

`\displaystyle{ \frac{2a}{ {a}^(2) - {3}^(2) } - \frac{a + 1 + a - 1}{ {a}^(2) - {1}^(2) } }`

`\displaystyle{ \frac{2a}{ {a}^(2) - 9} - \frac{2a}{ {a}^(2) - 1 } }`

`\displaystyle{ \frac{2a( {a}^(2) - 1) - 2a( {a}^(2) - 9) }{( {a}^(2) - 1)( {a}^(2) - 9)} }`

`\displaystyle{ \frac{ {2a}^(3) - 2a - {2a}^(3) + 18a }{( {a}^(2) - 1)( {a}^(2) - 9)} }`

`\displaystyle{ \frac{16a}{( {a}^(2) - 1)( {a}^(2) - 9) } }`

Explanation:

Answered by:-

`\frak{iuynsm}`