To determine the remainder of the given division problem, we start with analyzing the expressions and their values step by step.
1. The numerator of the division problem is given as [tex]\(1\)[/tex].
2. The denominator of the division problem is [tex]\( (x+1) \)[/tex].
3. We are also given that [tex]\( x = 0 \)[/tex].
4. Substituting [tex]\( x = 0 \)[/tex] into the denominator, we have [tex]\( x + 1 = 0 + 1 = 1 \)[/tex].
5. Now, the division problem reduces to [tex]\(\frac{1}{1}\)[/tex].
6. Performing the division, [tex]\( \frac{1}{1} = 1 \)[/tex].
7. Since the question asks for the remainder of the division, we must consider the remainder when dividing 1 by 1.
8. When 1 is divided by 1, the quotient is 1, and importantly, the remainder is [tex]\( 0 \)[/tex], because 1 divides evenly by 1 with no leftovers.
Therefore, the remainder of the division problem is [tex]\( 0 \)[/tex].
