Final answer:
Upon simplifying the expression √25(x-1) + √5(x-1)², we find that none of the provided options (A, B, C, D) match the simplified result of 6(x-1).
option b is the correct
Step-by-step explanation:
The student has asked which choice is equivalent to the quotient shown, with the expression being √25(x-1) + √5(x-1)². To find an equivalent expression, we need to simplify it. First, let's break down the square roots where possible. We know that √25 is 5 and the second term can be simplified because the square root and the square cancel each other out, leaving us with just (x-1).
Now, the expression looks like this: 5(x-1) + (x-1). Combining like terms, we add the coefficients in front of (x-1), resulting in 5 + 1 times (x-1), which simplifies to 6(x-1). We can see that none of the provided options directly match this, and the closest option B is incorrect because it has 5 instead of 6 as the coefficient. Hence, none of the given options are equivalent to the provided quotient for acceptable values of X.