Question

Solve:

`x/3 + 3/(6 - x) = (2(6 +x))/15; (x ≠ 6)`

Answer 1

`x/3 + 3/(6 - x) = (2(6 + x))/15; (x ≠ 6)`

⇒ `(x(6 - x) + 3 xx 3)/(3(6 - x)) = (12 + 2x)/15`    ....(Both equation dividing by 3) 

⇒ `(x(6 - x) + 3 xx 3)/(6 - x) = (12 + 2x)/5`

⇒ `(6x - x^2 + 9)/(6 - x) = (12 + 2x)/5`

⇒ 30x – 5x² + 45 = 72 + 12x – 12x – 2x²

⇒ 30x – 5x² + 45 = 72 – 2x²

⇒ 3x² – 30x + 27

⇒ x² – 10x + 9 = 0

⇒ x² – 9x – x + 9 = 0

⇒ x(x – 9) – 1(x – 9) = 0

⇒ (x – 9)(x – 1) = 0

⇒ x – 9 = 0 or x – 1 = 0

⇒ x = 9 or x = 1