Expert: Richard J. Raridon - 6/11/2008

Question
In multiplying fractions, the solution shows that they inverted the integers within parenthesis in the numerator.  Why can this be done?  For example, they had factored out to (1-5x) (1-x) over (x-2) (x-1), the next step they switched to (5x-1) (x-1) in the numerator.  This of course simplified the canceling procedure, however, my question is how can you just switch, how do I know when I can, is there a rule regarding this?  Thanks.


Answer
They didn't invert the integers which means turning things upside down.  They reversed the terms, since 5x is not an integer.  What they really did was say (1-5x) = -1(5x-1) and (1-x) = -1(x-1)
and since (-1)(-1) = 1, that gives you (5x-1)(x-1).
You're doing very well for age 12.