Find the limit value

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In this problem we directly can't substitute the value x=2 to the problem because if we do so then then value of the function become 0÷0 form which is undefined. Therefore we remove the factor that is (x-2) which is causing this problem. To remove (x-2) we represent the quadratic equation in factorized form. When we factorized the quadratic equation then in the numerator and denominator we get the value (x-2) present in both. We can cancel this value. After cancellation, there remain the value. Now if we substitute x=2 to this remaining function then it will not give 0÷0 form. So it is safe to substitute the value x=2 to the remaining function. After substituting the value we get the value of the limit .

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