> Back again...this chapter on algebraic fractions is > killing me. I've been working on trying to change > complex fractions into simple fractions...with not > much luck. I've attached the problem that's giving me > fits along with the work I've managed to do so far > and my thought process of where I think I should head > next...problem is when I head in that direction I end > up way off course. > As always, any guidance would be appreciated! > Thanks in advance! > Evan
For any such questions about basic algebraic manipulations where you are trying to ensure your understanding of the concepts involved, try the following: where an expression includes literals (such as letters of arbitrary or unknown value), just substitute some convenient numerical value. Evaluate the expression numerically and see if you always get that same result after you perform each operation which you are not confident about.
In your example:
1 - (x/y) _____________
1 - (x^2/y^2)
Arbitrarily select x = 6, and y = 2, then
1 - (6/2) ___________
1 - (36/4)
1 - 3 _____
1 - 9
2 / 8
Now you can substitute the same x = 6 and y = 2 in any succeeding manipulated version of the original expression, but it had better yield 1/4...otherwise, you have made an error. Caution: good idea to avoid using 0 or 1 or -1 as the arbitrary substitutes, because they "might" introduce erroneous or undefined operations (in your present example you certainly wouldn't want to try a verification using y = 0. Why not?).
The final reduction that your given expression should achieve is:
x + y
(which also equates to 1/4 for the suggested numerical substitutions)