The partial fraction decomposition of 28/ x^2−4 can be written in the form of f(x)/ x−2 + g(x)/ x+2, where f(x)? where g(x)?

The value of f(x) is - 7  , and  The value of g(x) is 7   .

Step-by-step explanation:

Given as :

The partial fraction fraction decomposition of

i.e  = +  

Or,    =

Or, 28 = f(x) × (x - 2) +  g(x) × (x + 2)

Now, put x = 2

So , 28 = f(x) × (2 - 2) +  g(x) × (2 + 2)

Or, 28 = 0 + 4 × g(x)

∴ g(x) = = 7

Now, put x = - 2

So , 28 = f(x) × ( - 2 - 2) +  g(x) × ( - 2 + 2)

Or, 28 = - 4 × f(x) + g(x) × 0

∴ f(x) = = - 7

Hence The value of f(x) is - 7  , and  The value of g(x) is 7   .  Answer

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step-by-step explanation: