[MOVED] How does this Cancel? (rational equation)

[d1zz]

(x-2)/x/(x-2)(x+2) = 1/x(x+2)

Please someone help me by clarifying how the second step is produced. I worked through many options but I cant get to that second step.

The way I see it is if a fraction is divided by a fraction then you would multiply the first fraction by the reciprocal of the second.

Please help.

 

[tkhunny]

I do not believe you have it written correctly. Add parentheses to calrify meaning. I think you mean \(\displaystyle \frac{x-2}{x(x+2)(x-2)}\). If this is so, then

\(\displaystyle \L\,\frac{x-2}{x(x+2)(x-2)}\,=\,\frac{x-2}{x-2}*\frac{1}{x(x+2)}\,=\,1*\frac{1}{x(x+2)}\,=\,\frac{1}{x(x+2)}\)

 

[arthur ohlsten]

I believe the problem is to reduce the following:
[x-2] / x
----------- = ? multiply top and bottom[numerator and denominator] by x;
[x+2][x-2] or invert denominator and multiply

[x-2]
------------- = ? cancel [x-2]'s
x[x+2][x-2]

1
--------- answer
x[x+2]