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2021-11-18

To calculate: The partial decomposition of $\frac{{x}^{2}-2x-21}{{x}^{3}+7x}$

Cherry McCormick

Beginner2021-11-19Added 23 answers

Calculation:

Consider the provided expression:

Here,

Factorize

So, the expression can be written as:

Here, in g (x), there are two factors, one linear and one quadratic. So, the expression can be decomposed as:

Here, Least Common Divisor is

Multiply both sides of (1) by the Least Common Divisor to clear fractions:

simplify to obtain:

Compare the coefficients of x,x? and constant terms:

Solve for A the equation

Substitute -3 for A in

Substitute the obtained values of A, B and Cin (1):

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