Algebra-Partial Fractions
Can you please help me with the following questions please, I don't understand them. I know the general rule about them.
Write the partial fraction decomposition of the rational expression.
(x^2+4x-1)/(x^2+3)^2
(4x^3+4x^2)/(x^2+5)^2
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Answers
The partial fraction decomposition of the first expression is: (x+1)/(x^2+3) - 1/(x^2+3). The partial fraction decomposition of the second expression is: x/(x^2+5) + 1/(x^2+5)^2. The general steps for decomposing a rational expression into partial fractions is to first factor the denominator and identify the individual factors. Then, you need to multiply each factor by a suitable form of the numerator so that you get a sum of terms which is equal to the original expression. For the first expression, you need to multiply (x+1) and -1 by (x+3), and for the second expression, you need to multiply x and 1 by (x^2+5).
