Question
$$x-\frac{5}{4} = x+\frac{4}{5}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-\frac{5}{4} &= x+\frac{4}{5}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20x-20\cdot\frac{5}{4} &= 20x+20\cdot\frac{4}{5}&& \text{cancel out the denominators} \\[1 em]20x-25 &= 20x+16&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ -25 }$ to the right} \\[1 em]20x-20x &= 16+25&& \text{simplify left and right hand side} \\[1 em]20x-20x &= 41&& \\[1 em]0 &= 41&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 41 } $ is FALSE, we conclude that the equation has no solution.
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