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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


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Solve the inequality(s)<br> 2c &gt; 2 <br> d/6 ≥ 1 <br> r + 9 ≤ 23
tatiyna
Divide both sides by 2 for the first one.
2c/2>2/2
c>1
simplify both sides for the second 1 
1/6d>=1
6*(1/6d).=(6)*(1)
d>=6
For the last one 
subtract 9 from both sides
r+9-9<=23-9   so  that r<=14
 Hope this helps!





6 0
3 years ago
Suzie made a mistake in the following problem. The mistake was made in Line ___. Only input the number of the first incorrect li
zalisa [80]

Answer:

Mistake in Line 2

Step-by-step explanation:

Line 1  

7(6) ÷ 5 + 42  

Line 2  

7(6) ÷ 5 + 16  

Line 3  

42 ÷ 5 + 16  

Line 4  

42 ÷ 21  

Line 5  

2

To simplify any expression we use order of operation

Line 1 is 7(6) ÷ 5 + 42  

Order of operation is PEMDAS

First we start with parenthesis

so we multiply 7(6) in line 2

7*6- 42

So Line 2 is 42 ÷ 5 + 42  

Hence there is a mistake in Line 2

3 0
3 years ago
If 18 is added to a certain number and the sum is divided by 6, the result is 1 more than 14 of the original number. Find the or
Katyanochek1 [597]
The original number is 72 


(18+x)/6 = 1+14 
1/6x + 3 = 1 + 14 (Distribute)
1/6x + 3 = (1+14) (Combine Like Terms)
1/6x + 3 = 15 
        - 3 = -3          (Subtract 3 From Both Sides)
1/6x = 12 
(1/6x)*6 = 12 * 6  (Multiply Both Sides By 6)
x = 72


5 0
3 years ago
Every day, 500 airplanes in San Francisco incur an additional 30 minutes of airport delays when flying into or out of the airpor
rusak2 [61]
A. San Francisco is the largest opportunity cost
4 0
3 years ago
Read 2 more answers
A line passes through A(3, 7), and B(-4, 9). Find the value of a if C(a, 1) is on the line.
marissa [1.9K]

Answer:

ANSWER

a=-32

EXPLANATION

If C(a,1) is on the line that passes through A(3, 7), and B(-4, 9), then the three points are collinear.

This implies that, when we find the slope using any two points, we should get the same re.  sorry couldnt finish

Step-by-step explanation:

5 0
3 years ago
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