1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Korolek [52]
3 years ago
6

Perform the following operations s and prove closure. Show your work.

Mathematics
1 answer:
nadezda [96]3 years ago
5 0

Answer:

1. \frac{x}{x+3}+\frac{x+2}{x+5} = \frac{2x^2+10x+6}{(x+3)(x+5)}\\

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16} = \frac{1}{(x+2)(x-4)}

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6} = \frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3} = \frac{1}{(x-2)(x-4)}

Step-by-step explanation:

1. \frac{x}{x+3}+\frac{x+2}{x+5}

Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)

=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\

Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)

Putting factors

=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}

Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}

Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)

Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)

Putting factors

\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}

Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)

\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}

=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}

Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}

Converting ÷ sign into multiplication we will take reciprocal of the second term

=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}

Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.

You might be interested in
BRAINLIEST ASAP! PLEASE HELP ME :)
WITCHER [35]

Answer:

sin⁴x - sin²x

sin²x(sin²x - 1)

(1 - cos²x)(1 - cos²x - 1)

(1 - cos²x)(-cos²x)

-cos²x + cos⁴x

cos⁴x - cos²x

4 0
3 years ago
Awser 14 for me please
never [62]
A sorry I can't see the image
6 0
3 years ago
Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur
Schach [20]
X: earn per  hour during the week
y: earn per hour during the weekend

13x + 14y = 250.90
15x + 8y = 204.70

Multiply the first equation by 4 and the second equation by 7

52x + 56y = 1003.6
105x + 56y = 1432.90

Subtract the first equation from the second:

 53x = 429.30

x = 429.30/ 53
x = 8.10

Solve any of the equation for y:

15x + 8y = 204.70

y = [204.70 - 15(8.10)]/8 = 10.40

y - x = 10.40 -8.10 = 2.30

Answer: she earns $2.30 per hour more during the weekend than during the week.


8 0
3 years ago
Read 2 more answers
What type of number is -421
ludmilkaskok [199]

Answer:

integers, rationals, irrational, real numbers, imaginary, and complex numbers.

3 0
2 years ago
Bryce is solving this problem.
zavuch27 [327]

Answer:

The answer is C

2.640 and 10,560

Step-by-step explanation:

264 * 410 = (264 * 400) + (264 * 10) = 105,600 + 2640 = 2.640 and 10,560

6 0
3 years ago
Other questions:
  • A large airplane (plane A) flying at 26,000 feet sights a smaller plane (plane B) travelling at an altitude of 24,000 feet. The
    13·1 answer
  • Which function is increasing?
    12·1 answer
  • Describe the similarities and differences in the solution of 2x -7 =15 and 2x - 7 < 15
    15·1 answer
  • Evaluate ab + c for a = 2, b = 3, and c = 4
    6·2 answers
  • I am trying to homeschool my 13 yr old daughter can anyone guide me on here?​
    10·1 answer
  • 2x + 3y = -6<br> -2x + 3y = 6<br><br> How do I graph it
    6·1 answer
  • Which property of addition is used in the expression?<br> 0.5+ (0.4+0.8) = (0.5 +0.4) + 0.8
    14·2 answers
  • There are 6 girls and 18 boys in the class. What percent of the students are girls?​
    8·1 answer
  • A function f(x) = x^2 - 4 has a domain as the set of integers
    6·1 answer
  • Write an expression that is equivalent to n + 2 (n+3)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!