Perform the indicated operation, and write each answer in lowest terms. 2x/5 + x/4

Verified step by step guidance

1. Identify the denominators in the expression: 5 and 4.
2. Find the least common denominator (LCD) of 5 and 4, which is the smallest number divisible by both denominators.
3. Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: for \(\frac{2x}{5}\) multiply numerator and denominator by 4, and for \(\frac{x}{4}\) multiply numerator and denominator by 5.
4. Add the two fractions by combining their numerators over the common denominator: \(\frac{2x \times 4}{20} + \frac{x \times 5}{20} = \frac{8x + 5x}{20}\).
5. Combine like terms in the numerator and simplify the fraction if possible by factoring and reducing to lowest terms.

Key Concepts

Adding Rational Expressions

Adding rational expressions involves combining fractions that contain variables. To add them, the denominators must be the same, so you find a common denominator before combining the numerators.

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For numerical denominators like 5 and 4, the LCD is their least common multiple, which is essential for rewriting fractions with a common denominator.

Simplifying Fractions

After performing operations on fractions, simplifying means reducing the fraction to its lowest terms by dividing numerator and denominator by their greatest common factor. This makes the expression easier to interpret and use.