Add or subtract, as indicated. See Example 4. 5 11———— - ——— 12x²y 6xy

Verified step by step guidance

1. Step 1: Identify the least common denominator (LCD) for the fractions. The denominators are \(12x^2y\) and \(6xy\).
2. Step 2: Determine the LCD by finding the least common multiple of the coefficients and the highest power of each variable present in the denominators. The LCD is \(12x^2y\).
3. Step 3: Rewrite each fraction with the LCD as the new denominator. For the first fraction, it is already \(12x^2y\). For the second fraction, multiply both the numerator and the denominator by \(2x\) to get \(\frac{11 \cdot 2x}{12x^2y}\).
4. Step 4: Subtract the numerators of the fractions, since the denominators are now the same. The expression becomes \(\frac{5 - 22x}{12x^2y}\).
5. Step 5: Simplify the expression if possible. Check if the numerator can be factored or simplified further.

Key Concepts

Fraction Operations

Understanding how to add or subtract fractions is essential in this problem. To perform these operations, one must find a common denominator, which allows for the fractions to be combined. In this case, the denominators are polynomials, so factoring and simplifying may also be necessary.

Factoring Polynomials

Factoring polynomials is crucial for simplifying expressions before performing operations. It involves breaking down a polynomial into its constituent factors, which can help in finding a common denominator or simplifying the overall expression. Recognizing common factors in the numerator and denominator can lead to easier calculations.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form, which is important for clarity and ease of calculation. This can include canceling common factors in fractions or combining like terms. Mastery of simplification techniques ensures that the final answer is presented in the most straightforward manner.