1.) Which real number cannot be in the domain of this function?
f(x) =
_3x-1_________
2x^2 - 5x + 2
2.) Simplify by removing a factor equal to 1:
4a - 6
3 - 2a
3.) Multiply, simplify:
x^3 + 8 X ..x^6 - 4x^5 + 4x^4
x^5 - 4x^3 . . . . .x^2 - 2x + 4
4.) Divide, simplify:
z^2 - 8z + 16 +. . . 3z + 12
z^2 + 8z + 16. . . . . . z^2 - 16
5.)
If f(x) = -2x. . and g(x) = x^2 - 9
. . . . ..x + 3 . . . . . . . . . . . 3 - x .............., write the simplified form of the product function f(g)(X) and identify its domain.
6.)
Identify the missing numerator in the statement below that would make the equation TRUE:
x - 20............-....?????????.........=.... 3
x^2 - 8x + 12.........x^2 - 8x + 12........x-2
7.)
Add, simplify the results:
4s + ...........s
s^2 - 16....s + 4
Sorry that its hard to read, but I'm fairly new to this and I was having trouble with it bunching together when I would use my 'space' key. Help would be very much appreciated!
Thanks in advance.
I'll do one more since I have to be up early tomorrow and its 3 AM .
Any way, I'll help you 'remove a factor equal to 1,' where you should be able to solve from there.
(4a - 6)/(3 - 2a)
Is equivalent to:
[2*(2a - 3)]/[2*(-a + 3/2)]
2/2 is just 1;
(2a - 3)/(-a + 3/2); you should be able to take it from here.
And I'm sure others you'll get prompt replies on your other questions soon.
3.
<-- Cancel the and an
<-- Cancel the and one
We should state that and to indicate the terms we cancelled. (Typically such problems only involve real numbers and since there is no real number x such that we may ignore that we cancelled this in stating the domain of the expression.)
-Dan
z^2 - 8z + 16 = (z - 4)^2
z^2 + 8z + 16 = (z + 4)^2
3z + 12 = 3(z + 4)
z^2 - 16 = (z - 4)(z + 4)
Thus, we have:
[(z - 4)^2/(z + 4)^2] + [(3(z + 4))/((z - 4)(z + 4))]
We'll work with the part in italics above;
It's clear that we can cancel a z + 4, and we have:
[(z - 4)^2/(z + 4)^2] + 3/(z - 4)
You could expand the [(z - 4)^2/(z + 4)^2], or keep it the way it is, whichever you prefer.
I'll do #7, since I assume Dan is doing #6.
(4s)/(s^2 - 16) + s/(s + 4)
Factor s^2 - 16;
(s - 4)*(s + 4)
(4s)/[(s - 4)*(s + 4)] + s/(s + 4)
Find a common denominator; multiply the two denominators and determine the numerator;
((x + 4)*(4s))/[(x - 4)*(x + 4)*(x + 4)]
(4s^2 + 16s)/[(x - 4)*(x + 4)^2] + [((x - 4)*(x + 4))*x]/[(x - 4)*(x + 4)^2]
Now, we have a common denominator. Yay!
Now add the numerator and divide it by the same denominator;
[x^2*(x + 4)]/[(x - 4)*(x + 4)^2]
Cancel a (x + 4);
Thus, the final answer: x^2/[(x - 4)*(x + 4)]
See the LaTeX tutorials at the beginning of this thread.
Actually I'm not. I've got too many posts to go through. New girlfriends are distracting and time consuming. (But worth the effort! )
-Dan
(x - 20)/(x^2 - 8x + 12) - Y/(x^2 - 8x + 12) = 3/(x - 2)
They made this easy by giving you the common denom;
Factor x^2 - 8x + 12;
(x - 6)*(x - 2)
Whatever is in the numerator, Y, we want the result to be 3*(x - 6) so we can cancel an (x - 6) and be left with 3/(x - 2)
So, (x - 20) - {expression here} = 3*(x - 6)
(x - 20) - {expression here} = 3*x - 18
Thus, we have
(x - 20) - (-2x - 2);
Plug the bold part in for Y and check that it works;
(x - 20)/(x^2 - 8x + 12) - (-2x - 2)/(x^2 - 8x + 12) = 3/(x - 2)
[(x - 20) - (-2x - 2)]/[(x^2 - 8x + 12)]
(3x - 18)/[(x - 6)*(x - 2)]
3(x - 6)/[(x - 6)*(x - 2)]
Cancel the (x - 6);
Thus, 3/(x - 2), which is what you were looking for.