Answer
See the explanation
Work Step by Step
To solve the equation \( \frac{3}{2x-1} = \frac{6}{3x+1} \) and reduce it to the form \( x = 3 \), we can follow these algebraic productions:
1. Cross-multiply to eliminate fractions:
\[ 3(3x + 1) = 6(2x - 1) \]
2. Expand and simplify both sides:
\[ 9x + 3 = 12x - 6 \]
3. Rearrange terms to isolate \( x \):
\[ 3 = 12x - 9x - 6 \]
\[ 3 = 3x - 6 \]
4. Add 6 to both sides:
\[ 9 = 3x \]
5. Divide both sides by 3:
\[ x = 3 \]
General heuristic rules used when performing algebraic simplifications include:
1. Combine like terms.
2. Distribute or factor expressions.
3. Isolate the variable by performing inverse operations.
4. Eliminate fractions by cross-multiplying.
5. Avoid dividing by zero.
6. Check solutions for extraneous roots.
