We have the rational expression

; to simplify it, we are going to try to find a common factor in the numerator, and, if we are luckily, that common factor will get rid of the denominator

.
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable

, and the least exponent of that variable is 1, so

will be the other part of our common factor. Lets put the two parts of our common factor together to get

.
Now that we have our common factor, we can rewrite our numerator as follows:

We are luckily, we have

in both numerator and denominator, so we can cancel those out:


We can conclude that the simplified version of our rational function is

.
Answer:
See Explanation
Step-by-step explanation:
Sample Response: No, the triangle is not possible. The triangle inequality rule states the sum of any two sides must be greater than the third side. 6 + 4 is 10, which is less than 11.
Answer:
The graph shifts 7 units left and 2 units up.
Step-by-step explanation:
In transformations, when a number is added or subtracted to "x" directly, that is the left/right shift.
When a number is added or subtracted outside of the "rest" of the equation, that is the up/down shift.
I learned transformations with these variables:

"a" - vertical stretch (a > 1) or compression (0 < a < 1)
"k" - horizontal stretch (0 < k < 1) or compression (k > 1)
"c" - translate left (+) or right (-)
"d" - translation up (+) or down (-)
The untranslated graph is centred around the origin f(x) = 1/x
f(x) begins 3 units right and 1 unit up of the untranslated graph.
g(x) is 4 units left and 3 units up of the untranslated graph.
y
g |
| f
-----------|------------ x
There is a 7 units translation left and 2 units translation up.
0.68 = 0.6 + .08 = 6 x 0.1 + 8 x .01
They should all equal 0.68 :)