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
4vir4ik [10]
3 years ago
13

What is the solution to the equation x+3/x+2=3+1/x

Mathematics
2 answers:
victus00 [196]3 years ago
8 0

Answer:

x=-1

Step-by-step explanation:

x+3

------- = 3 + 1/x

x+2

Get a common denominator on the right

3*x/x + 1/x

3x/x + 1/x = (3x+1)/x


x+3       3x+1

------- = ---------

x+2         x


We can use cross products to solve

(x+3) *x = (3x+1) * (x+2)

x^2+3x = 3x*x +x + 3x*2 +2

Simplifying

x^2 + 3x = 3x^2 +7x+2

Subtract x^2 from each side

x^2 -x^2 + 3x = 3x^2-x^2 +7x+2

3x = 2x^2 +7x+2

Subtract 3x from each side

3x-3x = 2x^2 +7x -3x+2

0 = 2x^2 +4x +2

Divide by 2

0 = x^2 +2x +1

Factor

0 = (x+1) (x+1)

Using the zero product property

x+1 =0

x=-1

marishachu [46]3 years ago
6 0

Answer:

The solution set is { -1 }.

Step-by-step explanation:

If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2))  we get:-

x(x + 3) = 3x(x + 2)  + x + 2

x^2 + 3x = 3x^2 + 6x + x + 2

0 = 3x^2 - x^2 - 3x + 6x + x + 2

2x^2 +4x + 2 = 0

2(x^2 + 2x + 1) = 0

2( x + 1)(x + 1) = 0

x = -1    Multiplicity 2

The solution set  only contains 1 * -1 . Elements in a set are not repeated

So   its {-1}  (answer)


You might be interested in
Four books, one each on physics, chemistry, mathematics, and biology are about to be stacked on a shelf. If the books are stacke
Tomtit [17]
25%
since there are 4 books, and only one is a mathematics book, there is a 1/4 chance.  in other words, 25%
7 0
3 years ago
Read 2 more answers
50 POINTS!!! PLEASE HELPPPPP<br> Plot 1 2/5, −1/2, and −2 1/10 on the number line.
maxonik [38]

Answer:

the answer is -1 1/5

Step-by-step explanation: 7/5

8 0
3 years ago
Read 2 more answers
Write the quadratic equation in standard form:<br> 3x2 – X – 4= -30<br> x
zhuklara [117]

Answer:

3x²-29x+4

Step-by-step explanation:

3x²-x-4=-30x

0=-30x-3x²+x+4

0=-3x²-29x+4

4 0
2 years ago
Solve the equation (1 + x²)dy +xydx= 0​
Tatiana [17]

Answer:

y=\frac{c}{\sqrt[]{x^2+1} }

Step-by-step explanation:

(1 + x²)dy +xydx= 0​

(1+x^2)dy=-xydx\\\frac{1}{y}dy=\frac{-x}{x^2+1}dx\\

Integrate both side

lny=-\frac{1}{2} ln(x^2+1)+c\\y=\frac{c}{\sqrt[]{x^2+1} }

7 0
3 years ago
Whats the sum of (-3)+(-5)​
Flura [38]

the answer is -8. have a nice day!⭐️

8 0
2 years ago
Read 2 more answers
Other questions:
  • Give an example of a function from the set of integers to the set of positive integers that is g
    8·1 answer
  • PLEASE HELP! I WILL MARK THE BRAINLIEST!
    7·1 answer
  • Find the sum of a finite geometric sequence from n = 1 to n = 8, using the expression −2(3)^n − 1.
    7·1 answer
  • List the following objects in order from lowest inertia to highest inertia: Earth, desk, baseball, fork, house, feather,
    14·1 answer
  • twelve athletes are running a race. a gold medal is to be given to the winner, a silver is to be given to the second place finis
    5·1 answer
  • Breanna wrote a number that is 4 units from 0 on the number line.
    12·1 answer
  • Consider the perimeter of a rectangle being 68 cm and the width being 4 less than the length. Write a linear relation in terms o
    8·1 answer
  • 5 ÷ 9/10 please answer this
    5·2 answers
  • Professors often attempt to determine if the submissions by the students are genuine or copied off the web sources. The program
    5·1 answer
  • Alex is ordering his girlfriend a bouquet of flowers for their anniversary. Roses cost $5 each and carnations cost $2 each. He w
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!