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vfiekz [6]
3 years ago
9

Simplify

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

The answer is

<h2>\frac{ {x}^{2}  + 2x}{2x - 4 }</h2>

Step-by-step explanation:

<h3>\frac{7xy}{ {x}^{2}  -  4x + 4 }  \div  \frac{14y}{x^{2}  - 4}</h3>

To simplify , factorize

x² - 4x + 4 and x² - 4

<u>For x² - 4x + 4</u>

Write - 4x as a difference

x² - 2x - 2x + 4

x( x - 2) - 2(x - 2)

(x - 2)(x - 2)

<u>For x² - 4</u>

use the formula

a² - b² = ( a+b)( a - b)

That's

x² - 4 = (x + 2)(x - 2)

So now we have

<h3>\frac{7xy}{(x - 2)(x - 2)}  \div  \frac{14y}{(x + 2)(x - 2)}</h3>

Change the division sign to multiplication sign and reverse the second fraction

That's

<h3>\frac{7xy}{(x - 2)(x - 2)}  \times  \frac{(x + 2)(x - 2)}{14y}</h3>

Simplify

We have

<h3>\frac{x}{(x  - 2)(x - 2)}  \times  \frac{(x + 2)(x - 2)}{2}</h3>

Reduce the expression with x + 2

That's

<h3>\frac{x}{x - 2}  \times  \frac{x + 2}{2}</h3>

Multiply the fractions

<h3>\frac{x(x + 2)}{2(x - 2)}</h3>

We have the final answer as

<h3>\frac{ {x}^{2} + 2x }{2x - 4}</h3>

Hope this helps you

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James is employed at Chase Bank and makes $32,000 annually. If 20% of his income goes to housing, how much does he spend on hous
alisha [4.7K]

Answer:

$6,400

Step-by-step explanation:

1) 20% of 32,000 goes to housing!

This can be written as 0.2 times 32,000

The value of: 0.2 x 32,000 equals 6,400!

That would be your answer ($6,400)

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3 years ago
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6

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What is 3/8 equal to in decimals..?
MrRissso [65]

Answer: 0.375

Step-by-step explanation:

Hey there! If you have any questions feel free to leave them in the comments below.

To find the answer you would divide the numerator by the denominator. \frac{3}{8} would be equal to 0.375

~I hope I helped you :)~

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3 years ago
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Alejandro wants to adopt a puppy from an animal shelter. At the​ shelter, he finds eight puppies that he​ likes: a male and fema
alexgriva [62]

Answer:

Hence the required probability is, 3/4

Step-by-step explanation:  

At the shelter, he likes :  

a male coolie, a female coolie, a male boxer, a female boxer, a male beagle, a female beagle, a male Labrador, and a female Labrador.  

Let, A denote the event of selecting a male coolie and B denote the event of selecting a male Labrador.  

P(A) = 1/8 = P(B)  

Here the probability of selecting a puppy except A & B is,  

P(AUB)c = 1 - P(AUB) = 1 - { P(A) + P(B) } = 1 - 1/8 - 1/8 = 3/4

7 0
3 years ago
Based on the graphs of f (x) and g(x), what must the domain of (f ⋅ g)(x) be?
bekas [8.4K]

Using the concept of domain, the domain of (f.g)(x) is given by:

{x ∈ ℝ | x ≠ 3}

---------------------

  • The domain of a function is given by all possible input values, that is, <u>on a graph, all values that the x-axis assumes.</u>
  • In the graph, <u>function f assumes all real values.</u>
  • Function g is not defined for x = 3, thus, it's domain is all real values except 3.
  • Thus, the multiplication, as fg(x) = f(x) \times g(x), will also not be defined at x = 3, and the domain of the multiplication is:

{x ∈ ℝ | x ≠ 3}

A similar problem is given at brainly.com/question/4175434

4 0
3 years ago
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