We have to determine whether the given problem is equation or expression. If it is an equation then we have to solve and if it is expression then simplify where problem is:

\(\displaystyle{\frac{{{5}{n}}}{{{6}}}}-{\frac{{{n}}}{{{8}}}}=-{\frac{{{17}}}{{{12}}}}\)

We know that

Expression can be any numbers, variables or combination of number and variable connected through mathematical operations.

Example:

\(\displaystyle{3},{x}^{{{2}}},{5}+{17}{x}\), ...

Equation is connected through equal sign where each side should be any expression.

Example:

\(\displaystyle{x}={y},{x}^{{{2}}}+{3}={0},{x}^{{{2}}}+{2}{x}={7}\), ...

The given problem have two expressions connected through equal sign.

Hence, it is an equation.

Step 2

Now solving the equation by taking LCM of the denominator in LHS side, we get

\(\displaystyle{\frac{{{5}{n}}}{{{6}}}}-{\frac{{{n}}}{{{8}}}}=-{\frac{{{17}}}{{{12}}}}\)

\(\displaystyle{\frac{{{5}{n}\times{4}-{3}\times{n}}}{{{24}}}}=-{\frac{{{17}}}{{{12}}}}\)

\(\displaystyle{\frac{{{20}{n}-{3}{n}}}{{{24}}}}=-{\frac{{-{17}}}{{{12}}}}\)

\(\displaystyle{\frac{{{17}{n}}}{{{24}}}}=-{\frac{{{17}}}{{{12}}}}\)

\(\displaystyle{12}\times{17}{n}=-{17}\times{24}\)

\(\displaystyle{n}={\frac{{-{17}\times{24}}}{{{12}\times{17}}}}\)

=-2

Hence, solution of the equation is n=−2.