1. The problem is to solve the equation without converting to decimals. 2. Since the user did not specify the exact equation, I will assume a common algebraic problem: solve for $x$ in $\frac{2x+4}{3} = \frac{x-1}{2}$. 3. The formula used is to eliminate denominators by multiplying both sides by the least common multiple (LCM) of the denominators. 4. Multiply both sides by 6 (LCM of 3 and 2): $$6 \times \frac{2x+4}{3} = 6 \times \frac{x-1}{2}$$ 5. Simplify each side: $$\cancel{3} \times 2 \times (2x+4) = \cancel{2} \times 3 \times (x-1)$$ $$2(2x+4) = 3(x-1)$$ 6. Distribute: $$4x + 8 = 3x - 3$$ 7. Subtract $3x$ from both sides: $$4x - 3x + 8 = 3x - 3x - 3$$ $$x + 8 = -3$$ 8. Subtract 8 from both sides: $$x + \cancel{8} - \cancel{8} = -3 - 8$$ $$x = -11$$ Final answer: $x = -11$