Find the value of x in (3x)/(x+2)=(2)/(x+2)

We are given the equation:

\[
\frac{3x}{x+2} = \frac{2}{x+2}
\]

### Step 1: Eliminate the denominators.
Since both sides of the equation have the same denominator \((x+2)\), we can multiply both sides of the equation by \((x+2)\) to cancel them out:

\[
3x = 2
\]

### Step 2: Solve for \(x\).
Now, we solve the linear equation \(3x = 2\):

\[
x = \frac{2}{3}
\]

### Final Answer:
The value of \(x\) is \(\frac{2}{3}\).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What would happen if \(x = -2\) in the original equation?
2. How do you solve equations with different denominators?
3. Can you apply this method to solve \(\frac{5x}{x-1} = \frac{3}{x-1}\)?
4. How does this process change if the equation had two different denominators?
5. What are the implications of having the same term in both the numerator and denominator?

**Tip:** Always check if variables in the denominator make the equation undefined (like \(x = -2\) in this case).

Find the value of x in (3x)/(x+2) = (2)/(x+2)

Discover how to solve the rational equation 3x/(x+2) = 2/(x+2) by eliminating denominators and solving the resulting linear equation. This problem covers key algebra concepts such as rational expressions and solving linear equations, suitable for students in Grades 7-9.

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