Simplify the complex fraction. $\frac{\left(\frac{10x-20}{x+8}\right)}{\left(\frac{x-2}{x+8}\right)}$

A) $8,x\ne -2,x\ne 10$
B) $2,x\ne -10,x\ne 8$
C) $10,x\ne -8,x\ne 2$
D) $-1,x\ne 0,x\ne 8$
E) $1,x\ne 0,x\ne 2$

To simplify the given complex fraction, divide the numerator by the denominator: $\frac{\left(\frac{10x-20}{x+8}\right)}{\left(\frac{x-2}{x+8}\right)}$ . Factoring out a 10 from the numerator of the top fraction gives $\frac{10(x-2)}{x+8}$ . Since both the top and bottom fractions have the same denominator $(x+8)$ , they cancel out, leaving $\frac{10(x-2)}{x-2}$ , which simplifies to 10, provided $x\ne 2$ to avoid division by zero and $x\ne -8$ to ensure the original denominators are not zero.