Problem 35 - College Algebra Essentials

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 resulting fraction after the addition is \(\frac{2x^{2} -x}{x^{2} +3x}\).

Step 1 - Adding the Numerators

Firstly, add the numerators of the two fractions as their denominators are the same. This is done by adding \(x^{2} -2x\) from the first fraction and \(x^{2} +x\) from the second fraction: \(x^{2} -2x + x^{2} +x\).

Step 2 - Simplification

The next step is to simplify the combined equation from Step 1. Combine like terms to simplify the equation. This leads to: \(2x^{2} -x\).

Step 3 - Writing the Final Fraction

The final step is to place the simplified numerator over the common denominator to obtain the final result. So, the resulting fraction is: \(\frac{2x^{2} -x}{x^{2} +3x}\).