Question

Please help with hegarty algebraic fractions and quadratic equations

Answer 1

`\huge \bf༆ Answer ༄`

Let's solve ~

• 
  `\sf (3)/(x) - (3)/(x + 4) = 1`

• 
  `\sf (3(x + 4) -3x )/(x(x + 4)) = 1`

• 
  `\sf (3x + 12-3x )/(x(x + 4)) = 1`

• 
  `\sf 12 = {x(x + 4)}`

• 
  `\sf {x}^(2) + 4x = 12`

• 
  `\sf{ {x}^(2) + 4x - 12 = 0 }`

• 
  `\sf{ {x}^(2) + 6x - 2x - 12 = 0}`

• 
  `\sf{x(x + 6) - 2(x + 6) = 0}`

• 
  `\sf(x - 2)(x + 6) = 0`

Hence,

• 
  `\sf x = 2 \: \: or \: \: x = - 6`