F(x)=7x-17/x^2+6x+9 solve using fractional decomposition

f(x) = 7/(x+3) -38/(x+3)²

Step-by-step explanation:

The denominator is a perfect square, so the decomposition to fractions will involve both a linear denominator and a quadratic denominator.

You can start with the form ...

... f(x) = B/(x+3) + A/(x+3)²

and write this sum as ...

... f(x) = (Bx +3B +A)/(x+3)²

Equating coefficients gives ...

... Bx = 7x . . . . . B = 7

... 3B +A = -17 . . . . the constant term

... 21 +A = -17 . . . . filling in the value of B

... A = -38 . . . . . . . subtract 21 to find A

Now, we know ...

... f(x) = 7/(x+3) -38/(x+3)²

both equations and proportions are better.

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