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3 years ago

1/5 (x + 3/5)- 4/5 = 5

Mathematics

2 answers:

Nostrana [21]3 years ago

7 0

X= 142/5 hehehejeheheheh

nikdorinn [45]3 years ago

6 0

Answer:

1/5 (x + 3/5)- 4/5 = 5

1/5x + 3/25 - 4/5 = 5

(5x + 3 -20)/25 = 5

5x - 17 = 125

x = 142/5

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

ozzi

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

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

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

$5b (x)= 20$

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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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