Is this consider a Partial Fraction

chihwei

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Is the equation factorisable to solve using partial fraction?

Kindly seek for math experts help.

Regards
Jeff

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Why would you want to do that? Can you see that A=0 and B=5 ?

Does the original question you were given involve integration?
 
Is the equation factorisable to solve using partial fraction?

Kindly seek for math experts help.

Regards
Jeff

View attachment 28611
I would say that this equation is about partial fractions! It's asking you to express the LHS as a sum of fractions. There are several methods you can use to find A and B; whatever method you use, formal or not, you will have created partial fractions.

But I don't know what you mean by calling the equation factorizable. Do you, mean, does the denominator [imath]s^2+4s+4[/imath] factorize as [imath](s+2)^2[/imath]? You can check that by expanding the square. Then Harry's first question will be obvious.

You put this under Differential Equations; we commonly see this used in integration (which would just go under Calculus), but the technique itself is merely algebra, and is taught to algebra students with no knowledge of calculus. But your question is independent of all that context; it can be answered on sight.
 
Since \(\displaystyle x^2+ 4x+ 2= (s+ 2)^2\), yes, you can have partial fractions with the those denominators. I hope it would be obvious that, "by inspection", A= 0 and B= 5!

If you need to see it calculated, \(\displaystyle \frac{A}{x+2}+ \frac{B}{(x+ 2)^2}=\)\(\displaystyle \frac{A(x+ 2)}{(x+ 2)^2}+ \frac{B}{(x+2)^2}= \)\(\displaystyle \frac{Ax+ 2A+ B}{(x+ 2)^2}= \frac{5}{(x+2)^2}\). Since there is no "x" term on the right, A= 0 and 2A+ B= B= 5
 
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