Answer:
Yes, they are equivalent.
One way you can check this is by substituting any number into x.
For example, x = 2:
• First equation :
![(-x)/(x + 1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/2wz1kehirvi5okai300nywyw2wtt6fgkt6.png)
⇒
![(-2)/(2 + 1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/47344sanrxc1nz8ilpccckh7l1fhmzywy7.png)
⇒
![(-2)/(3)](https://img.qammunity.org/2023/formulas/mathematics/college/kpct6u9pnxh5n9r5909keok3b1agech9iw.png)
• Second equation:
![(x)/(-x-1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/ek6vxq3ffvrr46hpdhm1tcqvcqh37lz0d3.png)
⇒
![(2)/(-2-1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/8wi2a49sh4e7cx9hw0n0itquiexn42hegd.png)
⇒
![(-2)/(3)](https://img.qammunity.org/2023/formulas/mathematics/college/kpct6u9pnxh5n9r5909keok3b1agech9iw.png)
As both forms of the equation give the same result after substitution, they are equivalent.