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
san4es73 [151]
3 years ago
12

Simplify f+g / f-g when f(x)= x-4 / x+9 and g(x)= x-9 / x+4

Mathematics
2 answers:
steposvetlana [31]3 years ago
6 0

f(x)=\dfrac{x-4}{x+9};\ g(x)=\dfrac{x-9}{x+4}\\\\f(x)+g(x)=\dfrac{x-4}{x+9}+\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)+(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2+x^2-9^2}{(x+9)(x+4)}=\dfrac{2x^2-16-81}{(x+9)(x+4)}=\dfrac{2x^2-97}{(x+9)(x+4)}\\\\f(x)-g(x)=\dfrac{x-4}{x+9}-\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)-(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2-(x^2-9^2)}{(x+9)(x+4)}=\dfrac{x^2-16-x^2+81}{(x+9)(x+4)}=\dfrac{65}{(x+9)(x+4)}


\dfrac{f+g}{f-g}=(f+g):(f-g)=\dfrac{2x^2-97}{(x+9)(x+4)}:\dfrac{65}{(x+9)(x+4)}\\\\=\dfrac{2x^2-97}{(x+9)(x+4)}\cdot\dfrac{(x+9)(x+4)}{65}\\\\Answer:\ \boxed{\dfrac{f+g}{f-g}=\dfrac{2x^2-97}{65}}

Lubov Fominskaja [6]3 years ago
6 0

Answer:

B. 2x^2 - 97 / 65


You might be interested in
Please Help!!!
Viefleur [7K]

Answer:

Numeric expressions apply operations to numbers. For example, 2(3 + 8) is a numeric expression. Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

Step-by-step explanation:

8 0
3 years ago
The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
Katena32 [7]
A triangle has three angles, and their measures add up to 180 degrees.
An isosceles triangle has at least 2 congruent sides, and the angles opposite the congruent sides are congruent.

This triangle has one angle of 40 deg, and two angles that measure the same; call the measure of each base angle x.

x + x + 40 = 180

2x + 40 = 180

2x = 140

x = 70

The base angles measure 70 deg.
8 0
3 years ago
Read 2 more answers
Solve the system of equations using any method.
stiv31 [10]

Answer:

My answer what I came up with is B And B

4 0
3 years ago
I give up math is hard
AlexFokin [52]

Answer:

3, 4, 6 and 8 are true.

Step-by-step explanation:

Check out the rules in below picture.

3 0
3 years ago
Help me out with this problem ?​
3241004551 [841]

Answer:

(-4.5, 2.5)

Step-by-step explanation:

The solution for two graphed linear equations is the intersection (The point where two lines meet or cross).

4 0
3 years ago
Other questions:
  • Three cards are chosen from a standard deck of 52 playing cards with replacement. What is the probability every card will be an
    9·1 answer
  • What is 6,459,821.891 rounded to the nearest hundred
    6·2 answers
  • 11 more than y please help
    15·1 answer
  • For the graph x = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your an
    5·1 answer
  • Factor each expression completely.<br> a. X^2- X-72
    9·1 answer
  • 48% is 50 percent more than what number?
    15·2 answers
  • I WILL GIVE BRAINLIEST!!!!!<br><br> Find an equation for the line below.
    14·2 answers
  • What is the probability of spinning green?
    12·1 answer
  • One hundred thirty people were asked to determine how many cups of fruit and water they consumed per day. the results are shown
    10·2 answers
  • Buying rental property is an investment option that carries a higher risk than some other options. However, the returns can be g
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!