CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x

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Identify the given expression as the sum of two fractions with the same denominator: \(\frac{3}{x} + \frac{7}{x}\).

Since the denominators are the same, combine the numerators directly over the common denominator: \(\frac{3 + 7}{x}\).

Add the numerators: \(3 + 7 = 10\), so the expression becomes \(\frac{10}{x}\).

Check if the fraction \(\frac{10}{x}\) can be simplified further by factoring numerator and denominator and canceling common factors.

Write the final simplified expression, ensuring it is in lowest terms.

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Adding Rational Expressions

Adding rational expressions involves combining fractions with variables in the denominators. To add them, you must find a common denominator, rewrite each fraction with this denominator, and then add the numerators while keeping the denominator the same.

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For variable denominators like 'x', the LCD is simply 'x' if both denominators are the same, which allows direct addition of the numerators.

Simplifying Rational Expressions

After performing the addition, simplify the resulting rational expression by factoring and reducing common factors in the numerator and denominator. This ensures the answer is in lowest terms, making it easier to interpret and use.