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Question
Solve:
`x/3 + 3/(6 - x) = (2(6 +x))/15; (x ≠ 6)`
Solution
`x/3 + 3/(6 - x) = (2(6 + x))/15; (x ≠ 6)`
⇒ `(x(6 - x) + 3 xx 3)/(3(6 - x)) = (12 + 2x)/15`
⇒ `(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
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