Whyou are 25 and 36 square numbers?

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

ikadub [295]

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

Factorize each denominator
Simplify each fraction to its lowest term
Find the LCM of the two denominators
Divide LCM by each denominator and multiply the numerators by its corresponding quotients
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 different factors 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 $\frac{2}{(x+1)(x+3)}$

5 0

3 years ago

Hazel knits 5 centimeters of scarf eachnight. After 5 nights of knitting, how manycentimeters of scarf will Hazel have knit into

natta225 [31]

Answer:

Hazel will have knitted 25 centimeters of the scarf

SOLUTION

Problem Statement

We are told Hazel knits 5 centimeters of scarf every night for 5 nights. We are required to find the length of the scarf Hazel will have knitted after 5 nights.

Solution

We are told Hazel makes 5 centimeters of scarf every night. Thus, for each night up till 5 nights, we just need to add the length of scarf Hazel has made.

Let us count for each night.

Night 1:

Hazel makes 5 centimeters of the scarf.

Night 2:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (5+5)\text{centimeters} \\ =10\text{ centimeters} \end{gathered}$

Night 3:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (10+5)\text{centimeters} \\ =15\text{ centimeters} \end{gathered}$

NIght 4:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (15+5)\text{centimeters} \\ =20\text{ centimeters} \end{gathered}$

NIght 5:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (20+5)\text{centimeters} \\ =25\text{ centimeters} \end{gathered}$

Final Answer

Thus, Hazel will have knitted 25 centimeters of the scarf

5 0

1 year ago

4x+6-3x=8-2x The answer comes up wrong if I put .6 or .66666 or .6666667

Anettt [7]

The answer would be x=2/3

4 0

3 years ago

Read 2 more answers

Find the equation of the line that is perpendicular to y=3/4x-3 and passes through the point (3,-2)

morpeh [17]

Answer:

Step-by-step explanation:

perp. -4/3

y + 2 = -4/3(x - 3)

y + 2 = -4/3x + 4

y = -4/3x + 2

4 0

3 years ago

Y=0.5x how do you work it

photoshop1234 [79]

Plug any number in for x and find the resulting y, then if you need to graph place the coordinate points on the plane. For example if you set x=2 the equation becomes y=0.5(2). From here we can see 0.5(2)=1 and this is equal to 1 so in a data chart you would write under x the number 1 and under y the number 2.

6 0

3 years ago