I have several doubts about notation. I would appreciate any clarifications.

a) I can express, for example, a periodic or semi-periodic number without writing it in its rational form. Can such notation be recognized by Mathematica?

Examples:

$$a= 0. \bar{8}, b= 1.34\bar{5}$$

b) If I do the a/b operation with the numbers above, how do I force Mathematica to write the result in a non-decimal rational form?

c) How do I solve the following equations involving nested radicals?

$$\sqrt{x+\sqrt{x+\sqrt{x+...}}}=12$$ $$\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-...}}}}=15$$

I have several doubts about notation. I would appreciate any clarifications.

a) I can express, for example, a periodic or semi-periodic number without writing it in its rational form. Can such notation be recognized by Mathematica?

Examples:

$$a= 0. \bar{8}, b= 1.34\bar{5}$$

b) If I do the a/b operation with the numbers above, how do I force Mathematica to write the result in a non-decimal rational form?

c) How do I solve the following equations involving nested radicals?

$$\sqrt{x+\sqrt{x+\sqrt{x+...}}}=12$$ $$\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-...}}}}=15$$

edit It seems that I did not express myself very well. If I have any rational decimal as a result, how can I get MMA to express it to me in the form a/b? Apologies for putting more than one question, I thought they were part of the same

I have several doubts about notation, if you could clarify me I would appreciate it

a)I can express, for example, a periodic or semiperiodic number without writing it in its rational form, and that form be recognized by MMA example $$a= 0. \bar{8}, b= 1.34\bar{5}$$

b)If I do the a/b operation with the numbers above, how do I force MMA to write the result in non-decimal rational form?

c)How do I solve equations like this?

$$\sqrt{x+\sqrt{x+\sqrt{x+...}}}=12$$ $$\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-...}}}}=15$$

I have several doubts about notation. I would appreciate any clarifications.

a) I can express, for example, a periodic or semi-periodic number without writing it in its rational form. Can such notation be recognized by Mathematica?

Examples:

$$a= 0. \bar{8}, b= 1.34\bar{5}$$

b) If I do the a/b operation with the numbers above, how do I force Mathematica to write the result in a non-decimal rational form?

c) How do I solve the following equations involving nested radicals?

$$\sqrt{x+\sqrt{x+\sqrt{x+...}}}=12$$ $$\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-...}}}}=15$$