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
tester [92]
2 years ago
7

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!​

Mathematics
1 answer:
Greeley [361]2 years ago
6 0

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

\frac{3}{x + 4}  - \frac{1}{x + 3}  = \frac{x + 9}{(x^2 + 7x + 12)}

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

\frac{3*(x + 4)}{x + 4}  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

3  - \frac{(x + 4)}{x + 3}  = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x + 3)

3*(x + 3)  - \frac{(x + 4)*(x+3)}{x + 3}  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

3*(x + 3)  - (x + 4)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

(2*x + 5)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}

Now we can multiply both sides by (x^2 + 7*x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)

(2*x + 5)*(x^2 + 7x + 12)  = (x + 9)*(x + 4)*(x+3)

Now we need to solve this:

we will get

2*x^3 + 19*x^2 + 59*x + 60 =  (x^2 + 13*x + 3)*(x + 3)

2*x^3 + 19*x^2 + 59*x + 60 =  x^3 + 16*x^2 + 42*x + 9

Then we get:

2*x^3 + 19*x^2 + 59*x + 60 - (  x^3 + 16*x^2 + 42*x + 9) = 0

x^3 + 3x^2 + 17*x + 51 = 0

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

You might be interested in
Identify the steeper line y = 3x + 4 or y = 6x + 11
VLD [36.1K]

Step-by-step explanation:

the steeper line is y = 6x + 11 because its gradient 6, is bigger than 3

5 0
2 years ago
Read 2 more answers
PLEASE HELP WITH THIS!!!<br><br><br>solve for h <br><br><br>6/h+=3
seropon [69]
Your answer is h=2.
Explanation:
Divide 6 by 3
6 0
3 years ago
Does the mixed number 4 3/4 make each equation true? Choose Yes or No for each equation.
Mila [183]

Answer:

1 is Yes, 2 is No, 3 is No, 4 is No

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
How does brainstorm,decide,work,enjoy help with motivation?​
Assoli18 [71]

Answer:

It helps because it gets you thinking. Personally, it would motivate me because that process itself is very helpful. Brainstorm will get you your idea, you can decide if you want to do it or not, then you work on it, and because you have the right attitude towards whatever you are working on, you'll enjoy it!

6 0
3 years ago
In the figure shown below, AC is parallel to DE with transversal BF
densk [106]

Answer:

<h3>X = 142°</h3><h3>Y = 38° </h3>

<em><u>Given </u></em><em><u>-</u></em><em><u> </u></em> AC is parallel to DE

angle 3y + 28 = angle X ( Vertically opposite angles are equal).

3y + 28 = X

X + Y = 180° ( supplementary angles).

3y - X = (-28)

Solving both the equation we get

multiply eq 1 with 3

3x + 3y = 540

-X + 3y = (-28)

subtracting

4x = 568

x = 142°

3y + 28 = 142

3y = 142 - 28

3y = 114

y = 38°

4 0
2 years ago
Other questions:
  • A class is selling magazines as a fundraiser of the 200 magazines sold, Ananda sold 1/8 of them. Gina sold 0.065 of the magazine
    14·2 answers
  • The slope of (0,0),(6,7)
    15·1 answer
  • Explain how modeling partial products can be used to find the products of greater numbers.
    11·1 answer
  • How do you solve this problem? 4a-3b+7a=
    7·1 answer
  • 4/18 is closest to: 1/2 or 1 whole
    8·2 answers
  • 13x+y=4 please help me on this!
    10·1 answer
  • What is the answer this is a math question
    15·1 answer
  • Determine relationship b/t two triangles
    13·2 answers
  • C-1 1/4&gt;-2 1/2 please help me
    9·1 answer
  • A surgery has a success rate of 75%. Suppose that the surgery is performed on 4 patients. What is the probability that the surge
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!