Question

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

Answer 1

Hint: We need to find the additive inverse of $\dfrac{2x-3}{3x+5}$ . We start to solve the given question by multiplying the given function in $x$ with the minus sign. Then, we need to simplify the function further to get the desired result.

Complete step by step solution:
We are given a function in $x$ and need to find the inverse of it. We will be solving the given question by changing the sign of the given function to obtain its inverse.
Additive inverse of the number is the negation or opposite of the original number. It is obtained by changing the sign of the original number.
Let us understand how to solve the given question through an example as follows,
Example: What is the additive inverse of $17\;$
The additive inverse of any number is obtained by simply changing the sign of the original number.
From the above, we need to change the sign of the given number.
Applying the same, we get,
$\Rightarrow -17$
$\therefore$ The Additive inverse of the number $17\;$ is $-17$
Now, we need to find the additive inverse of $\dfrac{2x-3}{3x+5}$
The additive inverse of any number is obtained by simply changing the sign of the original number.
From the above, we need to change the sign of the given number.
Multiplying the function with a minus sign, we get,
$\Rightarrow -\left( \dfrac{2x-3}{3x+5} \right)$
Multiplying the minus sign with the numerator of the function, we get,
$\Rightarrow \dfrac{-2x+3}{3x+5}$
Rearranging the terms in the numerator, we get,
$\Rightarrow \dfrac{3-2x}{3x+5}$
$\therefore$ The additive inverse of $\dfrac{2x-3}{3x+5}$ is $\dfrac{3-2x}{3x+5}$

Note: The additive inverse of the number upon addition with the original number must give a zero. Following the same, the result of the given question can be cross-checked as follows,
$\Rightarrow \dfrac{2x-3}{3x+5}+\dfrac{3-2x}{3x+5}$
$\Rightarrow \dfrac{2x-3+3-2x}{3x+5}$
$\Rightarrow 0$
The result attained is correct.