Question

Number of partial fractions in x^4-5x²+1/(x²+1)³ is

Answer 1

Answer:

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Answer 2

The given question is we have to find the number of partial fractions in

${x}^{4} - 5 {x}^{2} + 1 \div {( {x}^{2} + 1)}^{3}$

In algebra, the partial fraction decomposition is also called the partial fraction expansion.

The partial fraction expansion of a rational fraction is an operation that consists of expressing the fraction as a sum of nipolynomial and one or several fractions with a simpler denominator.

In order to find a partial fractions following steps are used

start with a proper rational expressions.

factor the bottom into linear factors.

write out a partial fraction for each factor.

multiply the whole equation by the bottom.

solve for coefficient.

partial fraction is obtained.

The general splitting of partial fraction is

$\frac{f(x)}{(a {x}^{2} + b)} = \frac{ax + b}{(a {x}^{2} + b) } + \frac{c}{cx + b}$

substitute the value in the above expression we get,

$\frac{ {x}^{4} - 5 {x}^{2} + 1 }{ { ({x}^{2} + 1)}^{3} } = \frac{ax + b}{ {x}^{2} + 1 } + \frac{cx + d}{ {( {x}^{2} + 1) }^{2} } + \frac{ex + f}{ {( {x}^{2} + 1)}^{3} }$

There fore, the partial fractions are obtained for the given expression.

The number of partial fractions obtained for the given expression is 3.

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