In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)

Verified step by step guidance

Identify the two rational expressions to be subtracted: $\frac{3x}{x-3} - \frac{x+4}{x+2}$.

Find the least common denominator (LCD) of the two fractions, which is the product of the distinct denominators: $(x-3)(x+2)$.

Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator accordingly: $\frac{3x(x+2)}{(x-3)(x+2)} - \frac{(x+4)(x-3)}{(x+2)(x-3)}$.

Combine the two fractions into a single fraction by subtracting the numerators over the common denominator: $\frac{3x(x+2) - (x+4)(x-3)}{(x-3)(x+2)}$.

Expand the numerators, simplify by combining like terms, and write the final expression as a single simplified rational expression.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including simplifying and performing operations like addition or subtraction, is essential for solving problems involving rational expressions.

Finding a Common Denominator

To add or subtract rational expressions, you must find a common denominator, typically the least common denominator (LCD). This involves factoring denominators and determining the smallest expression that both denominators divide into, allowing the expressions to be combined.

Combining and Simplifying Rational Expressions

After rewriting expressions with a common denominator, combine the numerators by addition or subtraction. Then, simplify the resulting rational expression by factoring and reducing common factors to express the answer in simplest form.

Recommended video:

Guided course