Final answer:
The expression (x²-1)/(5x²+5x) simplifies to (x - 1) / (5x) after factoring both the numerator and the denominator and canceling out common terms.
Step-by-step explanation:
The expression (x²-1)/(5x²+5x) can be simplified to an equivalent expression in lowest terms by factoring both the numerator and the denominator. First, we factor x² - 1 which is a difference of squares and can be factored into (x + 1)(x - 1). Then, we factor out the common factor of 5x in the denominator to get 5x(x + 1). The (x + 1) terms in the numerator and denominator cancel out, leaving us with the simplified expression (x - 1) / (5x). This is the expression in its lowest terms, as no further simplification can be made.