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sergeinik [125]
3 years ago
7

Find the least common denominator for these two rational expressions s^3/s^2-2s+1 -2/s^2-4s+3

Mathematics
2 answers:
lidiya [134]3 years ago
7 0

Answer:

s⁴-6s³+12s²-10s+3


Step-by-step explanation:

s³/(s²-2s+1) - 2/(s²-4s+3)

The denominators are (s²-2s+1) and (s²-4s+3). Since one is not a multiple of the other, the least common denominator will be their product.

(s²-2s+1)(s²-4s+3) = s⁴-4s³+3s²-2s³+8s²-6s+s²-4s+3

                             = s₄ +(-4s³-2s³)+(+3s²+8s²+s²)+(-6s-4s)+3

                              = s⁴-6s³+12s²-10s+3

Anuta_ua [19.1K]3 years ago
4 0

Answer: \bold{\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}}

<u>Step-by-step explanation:</u>

Factor both denominators to see which factors are missing from each denominator. Then multiply both fractions so they have the same LCD.

  \dfrac{s^3}{s^2-2s+1}+\dfrac{-2}{s^2-4s+3}

=\dfrac{s^3}{(s-1)(s-1)}+\dfrac{-2}{(s-1(s-3)}

=\dfrac{s^3}{(s-1)(s-1)}\bigg(\dfrac{s-3}{s-3}\bigg)+\dfrac{-2}{(s-1(s-3)}\bigg(\dfrac{s-1}{s-1}\bigg)

=\dfrac{s^4-3s^3-2s+2}{(s-1)(s-1)(s-3)}


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<h3>What are the types of roots of the equation below?</h3>

Here in the question it is given that,

  • the equation x⁴ - 81 = 0

By using algebraic identity, (a + b)(a - b) = a² - b², we get,  

⇒ x⁴ - 81 = 0                      

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⇒ (x² + 9)(x² - 9) = 0

  1. (x² -  9) = (x² - 3²) = (x - 3)(x + 3) [using algebraic identity, (a + b)(a - b) = a² - b²]
  2. x² + 9 = 0 ⇒ x² = -9 ⇒ x = √-9 ⇒ x= √-1√9 ⇒x = ± 3i

⇒ (x² + 9) = (x - 3i)(x + 3i)

Now the equation becomes,

[(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

Therefore x + 3, x - 3, x + 3i and x - 3i are the roots of the equation

To check whether the roots are correct multiply the roots with each other,

⇒ [(x - 3)(x + 3)][(x - 3i)(x + 3i)] = 0

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Hence Option B, that is Two Complex and Two Real which are x + 3, x - 3, x + 3i and x - 3i, are the types of roots of the equation x⁴ - 81 = 0.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: What are the types of roots of the equation below?

x⁴ - 81 = 0

A) Four Complex

B) Two Complex and Two Real

C) Four Real

Learn more about roots of equation here:

brainly.com/question/26926523

#SPJ9

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