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Gemiola [76]
3 years ago
9

Simplify; 1/x^2+5x+6 + 1/x^2+3x+2 pls I need a step by step solution urgently

Mathematics
1 answer:
ikadub [295]3 years ago
5 0

Answer:

The simplest form of  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}  is  \frac{2}{(x+1)(x+3)}

Step-by-step explanation:

To add two algebraic fractions do these steps

  1. Factorize each denominator
  2. Simplify each fraction to its lowest term
  3. Find the LCM of the two denominators
  4. Divide LCM by each denominator and multiply the numerators by its corresponding quotients
  5. Add the two fraction and simplify the last answer

To simplify \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}

Factorize each denominator

∵ The denominator of the first fraction is x² + 5x + 6

∵ x² = (x)(x)

∵ 6 = (2)(3)

∵ (2)(x) + (3)(x) = 5x ⇒ middle term

∴ x² + 5x + 6 = (x + 2)(x + 3)

∵ The denominator of the second fraction is x² + 3x + 2

∵ x² = (x)(x)

∵ 2 = (2)(1)

∵ (2)(x) + (1)(x) = 3x ⇒ middle term

∴ x² + 3x + 2 = (x + 2)(x + 1)

Find the LCM of the two denominators

∵ The denominators are (x + 2)(x + 3) and (x + 2)(x + 1)

- LCM is all the <u><em>different factors</em></u> multiplied together

∴ LCM of them is (x + 1)(x + 2)(x + 3)

- Divide LCM by each denominator

∵ (x + 1)(x + 2)(x + 3) ÷ (x + 2)(x + 3) = (x + 1)

- Multiply the numerator of the first fraction by (x + 1)

∵ (x + 1)(x + 2)(x + 3) ÷ (x + 2)(x + 1) = (x + 3)

- Multiply the numerator of the second fraction by (x + 3)

∴  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2} = \frac{x+1}{(x+1)(x+2)(x+3)}+\frac{x+3}{(x+1)(x+2)(x+3)}

- Add the numerators and write the answer as a single fraction

∴  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2} = \frac{2x+4}{(x+1)(x+2)(x+3)}

- Factorize the numerator by taking 2 as a common factor

∵ 2x + 4 = 2(x + 2)

∴  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2} = \frac{2(x+2)}{(x+1)(x+2)(x+3)}

- Simplify the fraction by dividing up and down by (x + 2)

∴  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2} = \frac{2}{(x+1)(x+3)}

The simplest form of  \frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+3x+2}  is  \frac{2}{(x+1)(x+3)}

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1. a. Students

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4. (7.46,11.50)

Step-by-step explanation:

1. The researcher is interested in finding out the average number of states in US that the students have visited.

The unit that is being observed to arrive at that conclusion is the Students. The observational unit for this study is  a. Students.

2. The variable of interest from the information above is the number of U.S. states visited. The observations recorded for this variable are in numbers which are numeric in nature. This implies that the variable is quantitative in nature.

Therefore, the answe  is d. number of U.S. states visited, quantitative

3. To test whether the average number of states all students at the author’s school have visited,

The null hypothesis (H o) is always given as the negation statement/null of what we wish to test.

So, we wish to test that the average is different from 16. Therefore, the null would be that the average is 16.

Answer  is a. H o: mu = 16, Ha: mu ≠ 16

4. A  95% confidence interval for the average number of states all students at the author’s school have visited can be calculated using the formula:

x  bar + or - 2 √s/n

=9.48 + or - 2 × 7.13/ √50

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The 95% confidence interval for the average number of states all students at the author’s school have visited is (7.46,11.50). The average falls betw 7.64 and 11.50.

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Answer:

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Step-by-step explanation:

Given:

You buy milk that contains 180 calories per 2 cups.

Now, to find the number of calories in 5.5 cups.

Let the number of calories in 5.5 cups be x.

As, in 2 cups there are 180 calories.

2 cups is equivalent to 180 calories.

Thus, the ratio would be 2:180.

So, in 5.5 cups there are x calories.

5.5 cups is equivalent to x calories.

Thus, the ratio would be 5.5:x.

Now, we set proportion to get the number of calories in 5.5 cups:

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\frac{2}{180} =\frac{5.5}{x}

<em>By cross multiplying we get:</em>

2x=990

<em>Dividing both sides by 2 we get:</em>

x=495.

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