Question

divide polynomials by x (no remainders)
divide the polynomials.
your answer should be a polynomial.
\\(\frac{x^2 + 2x}{x} = \\) \boxed{}

Explanation:

Step1: Split the fraction

We can split the fraction \(\frac{x^{2}+2x}{x}\) into two separate fractions: \(\frac{x^{2}}{x}+\frac{2x}{x}\).

Step2: Simplify each fraction

For \(\frac{x^{2}}{x}\), using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\) (here \(a = x\), \(m = 2\), \(n = 1\)), we get \(x^{2-1}=x\). For \(\frac{2x}{x}\), the \(x\) in the numerator and denominator cancels out, leaving \(2\).

Step3: Combine the results

Combining the two simplified terms, we have \(x + 2\).

Answer:

\(x + 2\)