Solve the equation and check the solution Enter your answers

Solve the equation and check the solution. (Enter your answers as a comma-separated list. Simplify your answers completely. If there is no solution, enter NO SOLUTION.) See Example 4. (Objective 2) Identify any extraneous values. (Enter your answers as a comma-separated list. Simplify your answers completely. If there are no extraneous values, enter NO SOLUTION.)

Solution

n/( n^2 -4) + (n+7)/(n+2) = (n-7)/(n-2)

n/( n^2 -4) + (n+7)/(n+2) - (n-7)/(n-2)

Taking (n-2)(n+2) as LCD

{ n +(n+7)(n-2) - (n-7)(n +2) }/(n^2 -4) =0

{ n+ n^2 +5n -14 - ( n^2 -5n -14) }/(n^2 -4) =0

{ n+ 10n}/(n^2 -4) =0

11n =0

n =0

No extraneous solution

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