In order to add or subtract (or "combine"),
algebraic fractions, a common
denominator is needed. (This is the same process you use when adding and
subtracting "regular number fractions").
1.
First, choose the least common
denominator (lcd).
This is the
smallest number that all
denominators can divide into. 2. If any denominator in the problem is already the lcd, the numerator of that fraction stays the same (because the adjustment would be a multiplication times 1). If any denominator in the problem is not the lcd, multiply that numerator and denominator by the same value that was needed to create the lcd.
3. Combine the problem into one fraction: 4. Combine like terms in the numerator and reduce the resulting fraction (if needed):
The least common denominator for this problem is 4y. Adjust the numerators by the same values that were needed to create the new denominators.
The common denominator is 6.
Be sure to watch out for ""(negative signs) when distributing. You should always write out your work. When you try to take shortcuts and do the work in your head, signs have a tendency to "disappear".
In this problem, the common denominator is already
set at 8. The "trouble spot" in this problem is distributing the
negative sign to the whole numerator of the second
fraction.
Do you see how easily you could have made a mistake if you didn’t write out the (
)?
In this problem, be careful with all of the
different variables.
In this problem, the common denominator is 2k+1.
