Question

The additive inverse of $\frac{2x-3}{3x+5}$ is:

• A. $\frac{3-2x}{3x+5}$
• B. $\frac{3x+5}{2x-3}$
• C. $\frac{3-2x}{-3x-5}$
• D. $\frac{2x-3}{-3x-5}$

Answer 1

The correct option is A $\frac{3-2x}{3x+5}$

The additive inverse of a number is what you add to a number so that the sum will be zero. In other words, the additive inverse of $x$ is another integer $y$, as long as the sum of $x+y=0$. For example, the additive inverse of $5$ is $-5$ because their sum $5+(-5)=0$.

Similarly, the additive inverse of the fraction $\frac{2x-3}{3x+5}$ is $-\left(\frac{2x-3}{3x+5}\right)$ or $\frac{3-2x}{3x+5}$ and their sum is determined as:

$\frac{2x-3}{3x+5}+\left(\frac{-3+2x}{3x+5}\right)=\frac{2x-3-3+2x}{3x+5}=\frac{0}{3x+5}=0$

Hence, the additive inverse of $\frac{2x-3}{3x+5}$ is $\frac{3-2x}{3x+5}$