Question

Express in simples (2x-10)/(x+8)×(x²-64)/(x²+3x-40)

A. 2(x - 8) / (x + 8)
B. 2(x + 8) / (x - 8)
C. 2(x - 8) / (x - 8)
D. 2(x + 8) / (x + 8)

Answer 1

To simplify the expression (2x-10)/(x+8)×(x²-64)/(x²+3x-40), we can factor the numerator and denominator and cancel out common factors, resulting in a simplified expression of 2.

Step-by-step explanation:

To simplify the expression (2x-10)/(x+8)×(x²-64)/(x²+3x-40), we start by factoring the numerator and denominator. The numerator, (2x-10), can be factored as 2(x-5) and the denominator, (x+8), cannot be factored further. Additionally, the denominator, (x²-64), can be factored as (x-8)(x+8) and the denominator, (x²+3x-40), can be factored as (x-5)(x+8).

After factoring, we can cancel out common factors. The (x-5) and (x+8) terms in the numerator and denominator cancel out, leaving us with 2(x-5)/(x-5). Finally, since (x-5)/(x-5) equals 1, the expression simplifies to 2.