Solve:- (x + 4)/(x - 4) + (x - 4)/(x + 4) = 3 (1)/(3) help mmmm ​

Question

Solve:-


`(x + 4)/(x - 4) + (x - 4)/(x + 4) = 3 (1)/(3)`


help mmmm
​

Answer 1

`\displaystyle{ (x + 4)/(x - 4) + (x - 4)/(x + 4) = 3 (1)/(3) }`

`\displaystyle{ \frac{ {(x + 4) }^(2) + {(x - 4)}^(2) }{(x + 4)(x - 4)} = (10)/(3) }`

`\displaystyle{ \frac{ {x}^(2) + 8x + {4}^(2) + {x}^(2) - 8x + {4}^(2) }{ {x}^(2) - {4}^(2) } = (10)/(3) }`

`\displaystyle{ \frac{ {2x}^(2) + 16 + 16 }{ {x}^(2) - 16 } = (10)/(3) }`

`\displaystyle{3( {2x}^(2) + 32) = 10( {x}^(2) - 16) }`

`\displaystyle{ {6x}^(2) + 96 = {10x}^(2) - 160 }`

`\displaystyle{ {10x}^(2) - 160 = {6x}^(2) + 96 }`

`\displaystyle{ {10x}^(2) - {6x}^(2) - 160 - 96 = 0 }`

`\displaystyle{ {4x}^(2) - 256 = 0}`

`\displaystyle{4( {x}^(2) - 64) = 0}`

`{x}^(2) - {8}^(2) = \displaystyle{ (0)/(4) }`

`\displaystyle{(x + 8)(x - 8) = 0}`

`\displaystyle{ \rm{either, \: x + 8 = 0............(1) }}`

`\rm{or ,\: x - 8 = 0...............(2)}`

From equation (1)

`x + 8 = 0`

`x = - 8`

From equation (2)

`x - 8 = 0`

`\displaystyle{x = 8}`

`\therefore{x=±8}`