\(x+\frac{9}{4}=\frac{1}{3}+\frac{1}{4}-\frac{1}{-5}-\left(-\frac{2}{3}\right)-\left(-\frac{1}{4}\right)+\frac{4}{5}\)
\(x+\frac{9}{4}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{2}{3}+\frac{1}{4}+\frac{4}{5}\)
\(x+\frac{9}{4}=\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{1}{4}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)\)
\(x+\frac{9}{4}=1+\frac{1}{2}+1\)
\(x+\frac{9}{4}=\frac{5}{2}\)
\(x=\frac{5}{2}-\frac{9}{4}\)
\(x=\frac{1}{4}\)