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\frac{n^{2}+m^{2}+2}{2mn}+\frac{2\times 2mn}{2mn}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2mn}{2mn}.
\frac{n^{2}+m^{2}+2+2\times 2mn}{2mn}
Since \frac{n^{2}+m^{2}+2}{2mn} and \frac{2\times 2mn}{2mn} have the same denominator, add them by adding their numerators.
\frac{n^{2}+m^{2}+2+4mn}{2mn}
Do the multiplications in n^{2}+m^{2}+2+2\times 2mn.
\frac{n^{2}+m^{2}+2}{2mn}+\frac{2\times 2mn}{2mn}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2mn}{2mn}.
\frac{n^{2}+m^{2}+2+2\times 2mn}{2mn}
Since \frac{n^{2}+m^{2}+2}{2mn} and \frac{2\times 2mn}{2mn} have the same denominator, add them by adding their numerators.
\frac{n^{2}+m^{2}+2+4mn}{2mn}
Do the multiplications in n^{2}+m^{2}+2+2\times 2mn.