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Resolve Into Partical Fraction :
[tex] \large\sf \frac{x + 4}{ {x}^{2} + x } [/tex]


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Sagot :

The partial fraction of [tex]\frac{x+4}{x^{2} +x}[/tex] is as follows

[tex]\frac{x+4}{x^{2} +x} =-\frac{3}{x+1}+\frac{4}{x}[/tex]

Partial fraction

Partial fraction is the result of writing a rational expression as the sum of two or more fractions.

Therefore,

[tex]\frac{x+4}{x^{2} +x} =\frac{A}{x+1}+\frac{B}{x}[/tex]

Let's find the zeros of (x + 1) and (x)

when x = -1

Ax + B(x + 1) = x + 4

x + 4 = A(-1) + B(-1 + 1)

-A = -1 + 4

A = -3

when x = 0

A(0) + B(0 + 1) = 0 + 4

B = 4

Therefore,

[tex]\frac{x+4}{x^{2} +x} =-\frac{3}{x+1}+\frac{4}{x}[/tex]

learn more on partial fraction here: https://brainly.com/question/24594390

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