`3/((x + 2)(x +5)) + 5/((x + 5)(x + 10)) + 7/((x + 10)(x + 17)) = x/((x + 2)(x + 17))`
`⇔ 1/(x + 2) - 1/(x + 5) + ...... + 1/(x + 10) - 1/(x + 17) = x/((x + 2)(x + 17))`
`⇔ 1/(x + 2) - 1/(x + 17) = x/((x + 2)(x + 17))`
`⇔ (x + 17)/((x + 2)(x + 17)) - (x + 2)/((x + 2)(x + 17)) = x/((x + 2)(x + 17))`
`⇒ x + 17 - x - 2 = x`
`⇒ x = 15`