The answer is: [tex] -\pi [/tex]
The explanation for this exercise is shown below:
1. By definition, a rational number can be written as a fraction, whose numerator and denominator are integers. The irrational numbers can't be written as a fraction.
2. [tex] \pi [/tex] is an irrational number, because you can't write it as a fraction. The only way to get a rational number with the sum of [tex] \pi [/tex] and other irrational number shown in the image attached, is that this number added be [tex] -\pi [/tex], because [tex] \pi -\pi =0 [/tex] and [tex] 0 [/tex] is a rational number.
