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Simplifying the numerator is all about breaking it down step by step. Let’s look at our example expression: \(\frac{8-5(2)}{6-4(3)}\). Start by focusing just on the numerator \(8 - 5(2)\). In this case, the operation inside the parentheses should be handled first. Multiply 5 by 2 to get 10. Now substitute 10 back into the expression: \(8 - 10\). Finally, perform the subtraction: 8 minus 10 equals -2. Thus, the numerator is now simplified to -2.
Breaking down problems into smaller steps like this makes simplifying much easier! Remember always to follow the order of operations, often remembered through PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Just like with the numerator, we simplify the denominator by taking it one step at a time. For our expression, the denominator is \(6 - 4(3)\). Start by dealing with the parentheses. Multiply 4 by 3 to get 12, and then plug this value back into the expression: \(6 - 12\). Finally, subtract 12 from 6, yielding -6. Now, the denominator is simplified to -6.
Always perform operations in the proper order and double-check your work for accuracy. This practice ensures that no steps are overlooked, leading to correct simplification every time.

When simplifying rational expressions, finding the Greatest Common Divisor (GCD) is essential. The GCD helps in reducing fractions to their lowest terms.
To simplify \(\frac{2}{6}\), determine the GCD of 2 and 6. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. For 2 and 6, the GCD is 2. Divide both the numerator and the denominator by their GCD: \(\frac{2 \div 2}{6 \div 2} = \frac{1}{3}\).
After dividing, the simplified expression is \(\frac{1}{3}\). Remember, identifying the GCD makes reducing fractions straightforward and helps in understanding and verifying your reductions.