"iL(6s-4)/((s-2)^(2) +16)" was answered by our experts

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Answered question

2022-03-24

iL(6s-4)/((s-2)^(2) +16)

Answer & Explanation

RizerMix

Expert2023-04-25Added 656 answers

We are given the expression $\frac{6 s - 4}{{(s - 2)}^{2} + 16}$ and we are required to simplify it.

We can start by expanding the denominator using the formula ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ . Here, $a = (s - 2) and b = 4$ .

Expanding the denominator, we get:

$({(s - 2)}^{2} + 4^{2}) = (s^{2} - 4 s + 4 + 16) = (s^{2} - 4 s + 20)$

Substituting this value in the original expression, we get:

$\frac{6 s - 4}{s^{2} - 4 s + 20}$

Now, we can factorize the denominator to simplify the expression further. We can use the quadratic formula to find the roots of the denominator, which are given by:

$s = \frac{4 \pm \sqrt{- 4 \cdot 1 \cdot 20}}{2 \cdot 1} = (4 \pm 2 \sqrt{5} i)$

Since the roots are complex, we cannot factorize the denominator further. Therefore, the expression is in its simplest form and cannot be simplified any further.

Hence, the simplified form of the expression $\frac{6 s - 4}{{(s - 2)}^{2} + 16}$ is $\frac{6 s - 4}{s^{2} - 4 s + 20}$ .

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