Question

simplify.
\frac{5}{x^2(x - 2)} + \frac{x}{x - 2}
\frac{x^3 + ?}{x^3 + \square x^2} +

Explanation:

Step1: Find common denominator

The common denominator is $x^2(x-2)$. Rewrite the second fraction:
$\frac{x}{x-2} = \frac{x \cdot x^2}{x^2(x-2)} = \frac{x^3}{x^2(x-2)}$

Step2: Add the two fractions

Combine the numerators over the common denominator:
$\frac{5}{x^2(x-2)} + \frac{x^3}{x^2(x-2)} = \frac{x^3 + 5}{x^2(x-2)}$

Step3: Expand the denominator

Multiply out the denominator terms:
$x^2(x-2) = x^3 - 2x^2$

Answer:

The missing value in the green box is $\boldsymbol{5}$, and the missing coefficient in the denominator is $\boldsymbol{-2}$. The fully simplified form is $\frac{x^3 + 5}{x^3 - 2x^2}$