algebra precalculus - Proof for square root series

$$\sum_{i=1}^x \frac{1}{\sqrt{2i-1}}-\frac{1}{\sqrt{2i+1}}= 1-\frac{1}{\sqrt{2x+1}}$$
I need to prove that the sums from the LHS are equal or at least equal to the terms from the RHS.

Is that possible?

I tried to solve it but I made some mistakes.

To be honest I have no idea if this is wrong or correct.

What are your suggestions?