Reduce each rational expression to lowest
terms. Assume that the variables represent only numbers for which the denominators are nonzero.
(a^2-b^2)/(a-b)
To reduce the rational expression (a^2 - b^2)/(a - b) to its lowest terms, we need to simplify the expression as much as possible.
First, notice that the numerator is a difference of squares: a^2 - b^2 = (a + b)(a - b). Therefore, we can rewrite the expression as:
((a + b)(a - b))/(a - b)
Next, we can cancel out the common factor of (a - b) in the numerator and denominator, resulting in:
(a + b)
So, the reduced expression is just (a + b).