\[ x = -\frac{12}{2 \times (-2)} = \frac{12}{4} = 3 \]

["Simplifying a Fraction Step-by-Step: Solving ( x = -\frac{12}{2 \ imes (-2)} = \frac{12}{4} = 3 )", "Mathematics often requires breaking down complex expressions into manageable, clear steps — especially when solving equations. One clear example involves simplifying the expression:", "[\nx = -\frac{12}{2 \ imes (-2)} = \frac{12}{4} = 3\n]", "In this article, we’ll explore how this equation simplifies step-by-step, highlighting key algebraic principles and ensuring clarity for learners at any level.", "---", "### Understanding the Expression", "At first glance, the equation:", "[\nx = -\frac{12}{2 \ imes (-2)} = \frac{12}{4} = 3\n]", "represents the simplification of a negative fraction divided by negative multiplication. Let’s unpack it clearly, matching each step logically.", "---", "### Step 1: Simplify the Denominator", "Start by evaluating the denominator:", "[\n2 \ imes (-2) = -4\n]", "This uses the rule of multiplying two negative integers, which yields a positive result multiplied by a negative sign:\n[\n2 \ imes (-2) = -4\n]", "---", "### Step 2: Rewrite the Original Expression", "Substitute the simplified denominator back:", "[\nx = -\frac{12}{-4}\n]", "Notice both the numerator and denominator are negative. When dividing two negatives, recall that:", "[\n\frac{-a}{-b} = \frac{a}{b}\n]", "But in this case, we have a negative sign before the fraction, so:", "[\n-\frac{12}{-4} = \frac{12}{4}\n]", "Because the negatives cancel out, turning the whole fraction into a positive.", "---", "### Step 3: Perform the Division", "Now simplify:", "[\n\frac{12}{4} = 3\n]", "This basic division confirms conclusively:", "[\nx = 3\n]", "---", "### Why This Simplification Matters", "Understanding how to simplify such expressions helps build strong foundational skills in algebra — such as:", "- Handling negative signs and multiplying/dividing integers\n- Applying fraction rules clearly and correctly\n- Recognizing equivalent forms for easier computation and verification", "Mastering these steps makes solving more complex equations far more approachable.", "---", "### Summary", "The computation:\n[\nx = -\frac{12}{2 \ imes (-2)} = \frac{12}{4} = 3\n]", "reduces neatly through:", "1. Multiply numerator and denominator by −1 to simplify the fraction\n2. Cancel opposite signs to make it positive\n3. Divide correctly to reach final integer result", "---", "### Key Takeaway", "When solving equations involving fractions and negative numbers, always simplify the denominator first, then handle signs carefully. Step-by-step simplification ensures accuracy and transparency — key for building confidence in mathematics.", "---", "Keywords: solving equations, fraction simplification, negative numbers, algebra example, step-by-step math, dividing by negative, how to simplify fractions, math learning tips", "---", "Need more practice? Try simplifying expressions like ( x = -\frac{-18}{6 \ imes 3} ) or check complex fractions to reinforce your skills!"]