We are given the equation:

\[
\frac{1}{z} - \frac{1}{2z} - \frac{1}{5z} = \frac{10}{z+1}
\]

### Step 1: Simplify the left-hand side (LHS)

Combine the terms on the left-hand side by finding a common denominator. Since all terms involve \( z \), we can directly subtract them.

\[
\frac{1}{z} - \frac{1}{2z} - \frac{1}{5z} = \frac{5}{5z} - \frac{2.5}{5z} - \frac{1}{5z}
\]
we

This page walks through solving the rational equation 1/z - 1/2z - 1/5z = 10/(z+1). It covers key concepts like simplifying fractions, finding common denominators, and solving for the variable in rational expressions. Suitable for students in Grades 8-10.

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