Question

Rewrite the expression 3√5x−2/5x-2³ , where x is not equal to 2³/5 , in a way that you can calculate the answer when x= 2³/5 . The answer will be written as u/v . What's u+v?

a) u−v
b) u+v
c) 2u
d) v−u

Answer 1

The expression is simplified using the properties of exponents to avoid undefined values at x=2³/5, then u and v are determined from the simplification and added for the final answer.

Step-by-step explanation:

The expression given 3√5x−2/5x-2³, simplifies to 3(x²)∙√5, because when x² is multiplied by itself, the result is x. To avoid undefined values when x=2³/5, the expression can be rewritten using the property of exponents: x² = √x. Therefore, if x=2³/5, the value of the expression can be computed as 3(2³/5)²∙√5. To find u and v for u/v, we must first compute this expression at x=2³/5, and then add u and v as required by the question.