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beks73 [17]
3 years ago
9

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

Mathematics
1 answer:
ozzi3 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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<h3>Answer:  8 = 4p   (choice A)</h3>

==================================================

Explanation:

p is a placeholder for a number. Think of it like a box where a number goes inside.

In this case, p is the price of one pack of pencils.

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---------------------------

Alternative method:

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Then replace the "4 packs" on the left hand side with "8 dollars"

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--------------------------

Yet another method:

We know it's $8 for 4 packs. This must mean it is 8/4 = 2 dollars per pack.

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