Simplify x²-2x+1/y-5 divided by x-1/y²-25?

Question

/ means it's a fraction
Simplify:

x²-2x+1/y-5 divided by x-1/y²-25

Answer 1

If you are doing your math homework, please try yourself and learn it, because you will need to know this for future math classes. If you don't learn it now, all future math classes are going to be a lot more difficult than they could have been if you learned this. So, the more you understand this, the easier other math classes will be.

If you still don't understand, ask someone for help (but not the answer), because having somebody explain it can still help you learn.

Anyways, here is the solution. As in your question, / is a fraction. Also x^2 means x to the second power also known as x squared.
The periods are just separators to make it more neat and organized, so ignore them.

If you multiply both the numerator and the denominator by the reciprocal of the denominator you get the following

x^2-2x+1/ (times) y^2-25/
....y-5 ....................... x-1
divided by
....x-1/.....(times).y^2-25/
..y^2-25...................x-1

This causes the denominator to cancel with the reciprocal you just multiplied it by, giving you:

x^2-2x+1/ (times) y^2-25/
.....y-5 ...................... x-1

Then when you combine the two fractions (because you are multiplying) and factor x^2-2x+1 and y^2-25 you get:

(x-1)*(x-1)*(y+5)*(y-5)/
.........(y-5)*(x-1)

Then you cancel one of the x-1 in the numerator and the x-1 in the denominator. Then do the same for y-5. This gives you:

(x-1)*(y+5)

And that is the most simplified answer.

Answer 2

Not even sure if I did it right, But my answer is x2-x+1/y2-20

Only way that I got that is I went with the elimation process. Not even sure if that is how you solve this problem. But it's really the only way, because most of the problem can not be divided by one another. For example the x2 can't be divided because there is not another one like it in the problem But hell if I got it wrong who cares, I tired. :)

Answer 3

[(x² - 2x + 1)/(y - 5)] / [(x - 1)/ (y² - 25)]
[(x² - 2x + 1)/(y - 5)] * [(y² - 25)/ (x - 1)]
[(x² - 2x + 1)/(y - 5)] * [(y + 5)(y - 5)/ (x - 1)]
[(x + 1)(x - 1)/(y - 5)] * [(y + 5)(y - 5)/ (x - 1)]
(x - 1)(y + 5)
xy + 5x - y - 5

Answer 4

(x-1)(x-1) x-1
-----------
y-5 y-5 y+5

Invert and multiply
x-1 x+1 y-5 y+5
---------
y-5 x-1

x+1 y+5-answer y-5 and x-1 cancel out

Answer 5

The phrase "the quantity" should tip you off that you have an intermediate step that is performed inside some parentheses. "five minus the quantity eight plus x" 5 - (8 + x)