Question

Solve the given problem

Answer 1

Given :

• 
  `(7)/(3x + 2) \: - (3)/(x + 6 ) = (1)/(x) \\`

To find :

• Value of ,'x'.

Solution :

• 
  `(7)/(3x + 2) \: - (3)/(x + 6 ) = (1)/(x) \\`

• 
  `\frac{(x + 6) *( 7) - (3x + 2) * (3)}{ {3x}^(2) + 20x + 12} = (1)/(x) \\`

• 
  `\frac{7x+ 42 - 9x - 6}{ {3x}^(2) + 20x + 12} = (1)/(x) \\`

• 
  `\frac{7x - 9x - 6 + 42}{ {3x}^(2) + 20x + 12} = (1)/(x) \\`

• 
  `\frac{ - 2x + 36}{ {3x}^(2) + 20x + 12} = (1)/(x) \\`

• 
  `- 2x {}^(2) + 36x= {3x}^(2) + 20x + 12`

• 
  `{3x}^(2) + 2x {}^(2) + 20x - 36x+ 12 = 0`

• 
  `5x {}^(2) - 16x+ 12 = 0`

• 
  `5x {}^(2) -6x -10x + 12 = 0`

• 
  `x (5x -6) - 2(5x-6)`

• 
  `(x -2)(5x -6)`

Therefore , The value of x would be either 2 or 6/5 .