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 
y = x^2 + 5x -3
y-x =2
Replace y in the second equation with the first one:
x^2 + 5x -3 - x = 2
Simplify by combining like terms:
x^2 + 4x -3 = 2
Subtract 2 from both sides:
x^2 + 4x -5 = 0
Fctor the polynomial:
(x-1) (x+5) = 0
Solve for both X's:
x = 1 and x = -5
Now replace x in the second equation with both value and solve for y:
y -1 =2, y = 3
y - -5 =2, y +5 = 2, y = -3
Now combine the sets of answers:
(1,3) and (-5,-3)
8 is in the ones place so 8 ones.
Given:
Two endpoints of a diameter of a circle:
P (-7, -10)
Q (3, 2)
a) To find the center of the circle, find the midpoint of the two points:
midpoint:
(x2 - x1 )/ 2 , (y2 - y1) / 2
x= (2 - (-7))/2 = 4.5
y= (3 - (-10))/2 = 6.5
Therefore, the center of the circle is at C(4.5, 6.5)
b) To find the radius of the circle, we need to find the distance between the two points and divide by 2.
d = √(y2-y1)^2 + (x2 - x1)^2
d = √(2-(-7))^2 + (3 - (-10))^2
d = 5√10 = diameter
r = d/2 = 5√10 /2
