General Idea:
When simplifying a rational expression, we need to do the below steps:
(i) Factor the Denominator of each fraction
(ii) Identify the Least Common Denominator (It is the product of prime factors involved with its highest exponent)
(iii) Identify and rewrite the equivalent fraction with the desired LCD.
(iv) Once the denominator are same, Combine the numerator.
Applying the concept:
What is the difference x/x^2-16-3/x-4
I assume that you mean to type the expression 
Step 1: Factoring 
Step 2: Identifying the LCD, we get 
Step 3: Rewriting the second fraction by multiplying x+4 on both top and bottom of second fraction so that we get the LCD.
![\frac{x}{x^2-16}-\frac{3}{x-4}=\frac{x}{(x+4)(x-4)} -\frac{3*(x+4)}{(x-4)*(x+4)} Step 4: Combine like terms since the denominators are same[tex] \frac{x-3(x+4)}{(x+4)(x-4)} =\frac{x-3x-12}{(x+4)(x-4)}=\frac{-2x-12}{(x+4)(x-4)} =\frac{-2(x+6)}{(x+4)(x-4)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bx%5E2-16%7D-%5Cfrac%7B3%7D%7Bx-4%7D%3D%5Cfrac%7Bx%7D%7B%28x%2B4%29%28x-4%29%7D%20%20%20-%5Cfrac%7B3%2A%28x%2B4%29%7D%7B%28x-4%29%2A%28x%2B4%29%7D%20%3C%2Fp%3E%3Cp%3EStep%204%3A%20Combine%20like%20terms%20since%20the%20denominators%20are%20same%3C%2Fp%3E%3Cp%3E%5Btex%5D%20%5Cfrac%7Bx-3%28x%2B4%29%7D%7B%28x%2B4%29%28x-4%29%7D%20%3D%5Cfrac%7Bx-3x-12%7D%7B%28x%2B4%29%28x-4%29%7D%3D%5Cfrac%7B-2x-12%7D%7B%28x%2B4%29%28x-4%29%7D%20%3D%5Cfrac%7B-2%28x%2B6%29%7D%7B%28x%2B4%29%28x-4%29%7D%20%20)
Conclusion:
In factored form the simplified expression 
In expanded form the simplified expression 
Answer:
58.2
Step-by-step explanation:
48.5*1.2=58.2
Step-by-step explanation:
<span>Part
A:
a) What do the x-intercepts and maximum value of the graph represent?
The x-intercepts are the distances at which the ball is on the ground.
First, at x = 0, that is when the ball is kicked; second, at x = 30, when the ball falls (return) to the ground.
b) What are the intervals where the function is increasing and decreasing,
and what do they represent about the distance and height? (6 points)
The function is increasing in the interval (0, 15) and is decreasing in the interval (15,30)
The increasing interval (0,15) is the horizontal distance from the point the the ball was kicked until it reached its highest altitude, this is where the ball was going upward.
The decreasing interval (15,30) is the horizontal distance from the point where the ball reached its highest altitude until it landed on the ground, this is where the ball was falling down.
Part B: What is an approximate average rate of change of the graph from x
= 22 to x = 26, and what does this rate represent
On the graph you can read that at x = 22, f(x) ≈ 12, and at x = 26 f(x) ≈ 7.
So, an approximate rate of change from x = 22 to x = 26 is given by the equation below:
change on f(x) 7 - 12
average rate of change = --------------------- = ----------- = -5/4
change of x 26 - 22
That rate represents that the ball fell about 5 ft per 4 ft in that interval.
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