Is there any website/software that let's me compare two mathematical statements and let me know if both are equivalent?

Sometimes when I am doing my maths homework I sometimes get confused and then decide to make two mathematical statements and then plug some numbers in them to see if the results match. For example :

$$\frac{\sqrt{x}}x = \frac{1}{\sqrt{x}}$$

Is there any website/software that lets me type the left hand side and the right hand side of the above equation and then tells me if these two are equivalent statements or not(like telling me in the form of true and false) I searched but was unable to find any, so if you know it then the answer would be appreciated. Thnx in advance. Note: Since I am an Idiot and Newbie I was unable to find the relevant tags for the question.

Solution 1:

Perhaps surprisingly, the answer is no in general. For a certain fairly natural class of expressions, it is undecidable whether a particular expression $E$ satisfies the equation $E = 0$. This is Richardson's theorem. Knowing whether $E1=E2$ is the same as knowing whether $E=E1-E2=0$.

Of course, in any particular case, you may well be able to find an argument as to why two expressions are equal. In your case you could obviously multiply top and bottom by $\sqrt{x}$. WolframAlpha will also help you.