I have included a link here. The other side of the equals sign I have no idea how they are coming up with 2x-3(x-3) after factoring it out. One the other side multiplying the fraction cancelled it out, but here it looks like they only canceled it out from the denominator but it seems like it is still there. I just have no idea where they are coming up with that part of the equation and they don't explain the factoring in the video.
http://www.wtamu.edu/academic/anns/mps/m…
http://www.wtamu.edu/academic/anns/mps/m…
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Hi,
. 3 . . . . x . . . 3
------ = ------- - ------
x - 3 . . x - 3 . .2
Multiply every fraction by the LCD of the denominators, 2(x - 3)
2(x - 3)3 . . . . 2(x - 3)x . . . 2(x - 3)3
. . ---------- = . . . . --------- - . . . . ---------
. . . x - 3 . . . . . . .x - 3 . . . . . . . 2
In the first fraction, the (x - 3) cancels, leaving 2(3) = 6.
In the second fraction, the (x - 3) cancels, leaving 2(x) = 2x.
In the third fraction, the 2 cancels, leaving (x - 3)3 behind the minus sign.
6 = 2x - (x - 3)3
Re-write with the 3 in front of the parentheses.
6 = 2x - 3(x - 3)
Distribute -3 through the parentheses.
6 = 2x - 3x + 9
Combine like terms to change 2x - 3x into -x.
6 = -x + 9
Subtract 9 from both sides.
6 - 9 = -x + 9 - 9
Combine like terms.
-3 = -x
Divide by -1 to get x alone.
3 = x
Once you get an answer, you have to substitute it back into the original equation to see if it works, or if it is an extraneous root, a number that doesn't work because it make a denominator equal to zero. Plug x = 3 into the original equation.
. 3 . . . . x . . . 3
------ = ------- - ------
x - 3 . . x - 3 . .2
. 3 . . . . 3 . . . 3
------ = ------- - ------
3 - 3 . . 3 - 3 . .2
3 . . . 3. . 3
---- = ---- - ---
0 . . . 0. . 2
Since you can't divide 3 by 0, this doesn't work, so discard the answer x = 3. It is extraneous. Since there is no other answer to check, there is no answer that works for this problem. There is no solution.
I hope that helps!! :-)
. 3 . . . . x . . . 3
------ = ------- - ------
x - 3 . . x - 3 . .2
Multiply every fraction by the LCD of the denominators, 2(x - 3)
2(x - 3)3 . . . . 2(x - 3)x . . . 2(x - 3)3
. . ---------- = . . . . --------- - . . . . ---------
. . . x - 3 . . . . . . .x - 3 . . . . . . . 2
In the first fraction, the (x - 3) cancels, leaving 2(3) = 6.
In the second fraction, the (x - 3) cancels, leaving 2(x) = 2x.
In the third fraction, the 2 cancels, leaving (x - 3)3 behind the minus sign.
6 = 2x - (x - 3)3
Re-write with the 3 in front of the parentheses.
6 = 2x - 3(x - 3)
Distribute -3 through the parentheses.
6 = 2x - 3x + 9
Combine like terms to change 2x - 3x into -x.
6 = -x + 9
Subtract 9 from both sides.
6 - 9 = -x + 9 - 9
Combine like terms.
-3 = -x
Divide by -1 to get x alone.
3 = x
Once you get an answer, you have to substitute it back into the original equation to see if it works, or if it is an extraneous root, a number that doesn't work because it make a denominator equal to zero. Plug x = 3 into the original equation.
. 3 . . . . x . . . 3
------ = ------- - ------
x - 3 . . x - 3 . .2
. 3 . . . . 3 . . . 3
------ = ------- - ------
3 - 3 . . 3 - 3 . .2
3 . . . 3. . 3
---- = ---- - ---
0 . . . 0. . 2
Since you can't divide 3 by 0, this doesn't work, so discard the answer x = 3. It is extraneous. Since there is no other answer to check, there is no answer that works for this problem. There is no solution.
I hope that helps!! :-)
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I really don't want to watch the video, but if you think it is wrong, then maybe it is. Work it out for yourself to your satisfaction, try to tear down your work by looking for errors. If you are just wondering about technique, do the same thing.
Unfactoring would be 2x - 3x + 9 or 9 - x.
This does not look very interesting. If you put more information in your question, it would get a quicker reply from most readers. Put in the original expression along with the expression you are questioning.
Unfactoring would be 2x - 3x + 9 or 9 - x.
This does not look very interesting. If you put more information in your question, it would get a quicker reply from most readers. Put in the original expression along with the expression you are questioning.
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what is the algebraic equation to find future numbers in this series
3 - 8
4 - 11
5 - 14
6 - 17
3 - 8
4 - 11
5 - 14
6 - 17