Which of the expressions below would you need to multiply by in order to get common denominators? \( \frac{x-1}{x+4}+\frac{x+5}{x-2} \) Only the first expression. Only the second expression. Neither expression. Both expressions.

To get a common denominator for the fractions \( \frac{x-1}{x+4} \) and \( \frac{x+5}{x-2} \), you'll need to identify a common factor that can be used for both. The denominators \( x+4 \) and \( x-2 \) do not share any common factors, so you'd multiply each fraction by the denominator of the other. This means both expressions need to be adjusted, leading to the conclusion that you would need to multiply by both. When combining fractions, it's important to remember that changing the denominators requires recalibrating the numerators accordingly. For instance, if you multiply \( \frac{x-1}{x+4} \) by \( x-2 \) and \( \frac{x+5}{x-2} \) by \( x+4 \), you'll find that you now have the same denominator, making the addition possible!