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beks73 [17]
2 years ago
9

Partial fraction decomposition 20x+9/25x^2+20x+4

Mathematics
1 answer:
ozzi2 years ago
6 0

Step-by-step explanation:

We have

\frac{20x + 9}{25 {x}^{2} + 20x + 4 }

Let's factor the denomiator first,

the denomaitor is a perfect square so we get

\frac{20x + 9}{(5x + 2) {}^{2} }

Now, we must think of two fractions that

\frac{a}{(5x + 2) {}^{2} }  +  \frac{b}{5x + 2}

We use a perfect square term for one fraction, then a linear one for the next, because if we set both of the denomiator to the same factor, we would get a inconsistent system.

So right now, we have

\frac{a}{(5x + 2) { }^{2} }  +  \frac{b}{5x + 2}  =  \frac{20x +9 }{25 {x}^{2} + 20x + 4 }

a + (5x  + 2)b = 20x + 9

5b (x)= 20

a + 2b = 9

b = 4

so that means that a is

a + (2)(4) = 9

a + 8 = 9

a = 1

So our equation is

\frac{1}{(5x + 2) {}^{2} }  +  \frac{4}{5x + 2}

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