Problem 35 - College Algebra

Question

Add or subtract as indicated. $$\frac{x^{2}-2 x}{x^{2}+3 x}+\frac{x^{2}+x}{x^{2}+3 x}$$

Step-by-Step Solution

Answer

The simplified form of the given expression is \( \frac{2x^{2} -x }{x^{2}+3x} \).

Step 1: Identify the Denominators

In the expression \( \frac{x^{2}-2 x}{x^{2}+3 x}+\frac{x^{2}+x}{x^{2}+3 x} \), identify the denominators of both fractions. You can see that both have the same denominator \( x^{2} + 3x \).

Step 2: Carry out the Addition of Numerators

Since the denominators are the same, we can directly add the numerators. When adding \( (x^{2}-2x) \) and \( (x^{2}+x) \), you need to add the similar terms. This leads to \( 2x^{2} - x \).

Step 3: Write the Final Answer

The final answer will have the new numerator and the common denominator, leading to a final result of \( \frac{2x^{2} -x }{x^{2}+3x} \).