**Opgave 4:**

**Determine the value of the following expression knowing that m=-1 and n=2**


**5m/(2m^2+3mn)**

To determine the value of the expression given that \( m = -1 \) and \( n = 2 \), we substitute these values into the expression.

The expression is:

\[
\frac{5m}{2m^2 + 3mn}
\]

Substitute \( m = -1 \) and \( n = 2 \):

\[
\frac{5(-1)}{2(-1)^2 + 3(-1)(2)}
\]

Now, let's simplify this step by step.

1. Calculate the numerator:

\[
5(-1) = -5
\]

2. Calculate the denominator:
   - First, \( (-1)^2 = 1 \)
   - Then, \( 2(1) = 2 \)
   - Next, \( 3(-1)(2) = -6 \)

So, the denominator is:

\[
2 + (-6) = 2 - 6 = -4
\]

Now, substitute these into the expression:

\[
\frac{-5}{-4} = \frac{5}{4}
\]

So, the value of the expression is \( \frac{5}{4} \).

Would you like any further details or have any questions?

Here are 5 related questions for further practice:
1. What is the value of the expression \( \frac{3m}{4m^2 + 5mn} \) when \( m = 2 \) and \( n = -1 \)?
2. Simplify \( \frac{7m}{3m^2 + 2mn} \) given \( m = 1 \) and \( n = 4 \).
3. How does the expression change if both \( m \) and \( n \) are squared?
4. What is the value of \( \frac{4m}{m^2 - mn} \) when \( m = 3 \) and \( n = 2 \)?
5. Determine the value of \( \frac{6m}{2m^2 + 4mn} \) when \( m = -2 \) and \( n = 1 \).

**Tip:** Always check the signs of the numbers after substitution to avoid mistakes in calculations.

Learn how to evaluate the expression 5m/(2m^2 + 3mn) with m = -1 and n = 2 using substitution and simplification. This problem involves algebraic manipulation of linear equations and fractional expressions, suitable for students in Grades 7-9.

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