Answer:
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 [tex]\frac{28}{x^{2} - 4}[/tex]
i.e [tex]\frac{28}{x^{2} - 4}[/tex] = [tex]\frac{f(x)}{x-2}[/tex] + [tex]\frac{g(x)}{x+2}[/tex]
Or, [tex]\frac{28}{x^{2} - 4}[/tex] = [tex]\frac{f(x)\times (x-2) + g(x)\times (x+2)}{x^{2}-4}[/tex]
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) = [tex]\frac{28}{4}[/tex] = 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) = [tex]\frac{28}{ - 4}[/tex] = - 7
Hence The value of f(x) is - 7 , and The value of g(x) is 7 . Answer
