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) + 3 xx 3)/(3(6 - x)) = (12 + 2x)/15`

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

`=> 30x - 5x^2 + 45 = 72 - 2x^2`

`=> 3x^2 - 30x + 27  = 0`

`=> x^2 - 10x + 9 = 0`

`=> x^2 - 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