To simplify the expression \( 2z + \frac{6}{z+1} - \frac{5}{z+1} \), follow these steps:

1. Combine the two fractions that have the same denominator:
   \[
   2z + \frac{6 - 5}{z+1}
   \]

2. Subtract the numerators in the fraction:
   \[
   2z + \frac{1}{z+1}
   \]

So, the simplified expression is:
\[
2z + \frac{1}{z+1}
\]

Would you like any further details or have any questions?

Here are some related questions you might find useful:

1. How would you simplify \(3z + \frac{8}{z+2} - \frac{3}{z+2}\)?
2. What is the simplified form of \(4x + \frac{7}{x-1} + \frac{2}{x-1}\)?
3. Can you simplify \(5y + \frac{9}{y+3} - \frac{4}{y+3}\)?
4. How do you simplify \(x + \frac{5}{x-2} - \frac{3}{x-2}\)?
5. Simplify the expression \(2t + \frac{10}{t+4} - \frac{6}{t+4}\).

**Tip:** When working with algebraic fractions, always look for common denominators to simplify the expression.

Learn how to simplify the expression 2z + 6/(z+1) - 5/(z+1) step-by-step. This problem involves algebraic manipulation of fractional expressions. Suitable for high school students.

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