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Question
Select the correct answer from the given alternatives.
`lim_(x -> 3) (1/(x^2 - 11x + 24) + 1/(x^2 - x - 6))` =
Options
`-2/25`
`2/25`
`7/25`
`-7/25`
Solution
`lim_(x -> 3) (1/(x^2 - 11x + 24) + 1/(x^2 - x - 6))` = `-2/25`
Explanation:
`lim_(x -> 3) (1/(x^2 - 11x + 24) + 1/(x^2 - x - 6))`
= `lim_(x->3)[1/((x - 8)(x - 3)) + 1/((x - 3)(x + 2))]`
= `lim_(x->3)(2 x - 6)/((x - 8)(x - 3)(x + 2))`
= `lim_(x->3)(2)/((x - 8)(x + 2))`
= `-2/25`
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