Evaluate
\frac{2m+5n-14}{10\left(m-2\right)\left(n-2\right)}
Expand
\frac{2m+5n-14}{10\left(m-2\right)\left(n-2\right)}
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\frac{1}{2m-4}+\frac{1}{5n-10}\times 1
Divide 4n-8 by 4n-8 to get 1.
\frac{1}{2m-4}+\frac{1}{5n-10}
Express \frac{1}{5n-10}\times 1 as a single fraction.
\frac{1}{2\left(m-2\right)}+\frac{1}{5\left(n-2\right)}
Factor 2m-4. Factor 5n-10.
\frac{5\left(n-2\right)}{10\left(m-2\right)\left(n-2\right)}+\frac{2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(m-2\right) and 5\left(n-2\right) is 10\left(m-2\right)\left(n-2\right). Multiply \frac{1}{2\left(m-2\right)} times \frac{5\left(n-2\right)}{5\left(n-2\right)}. Multiply \frac{1}{5\left(n-2\right)} times \frac{2\left(m-2\right)}{2\left(m-2\right)}.
\frac{5\left(n-2\right)+2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)}
Since \frac{5\left(n-2\right)}{10\left(m-2\right)\left(n-2\right)} and \frac{2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)} have the same denominator, add them by adding their numerators.
\frac{5n-10+2m-4}{10\left(m-2\right)\left(n-2\right)}
Do the multiplications in 5\left(n-2\right)+2\left(m-2\right).
\frac{5n-14+2m}{10\left(m-2\right)\left(n-2\right)}
Combine like terms in 5n-10+2m-4.
\frac{5n-14+2m}{10mn-20m-20n+40}
Expand 10\left(m-2\right)\left(n-2\right).
\frac{1}{2m-4}+\frac{1}{5n-10}\times 1
Divide 4n-8 by 4n-8 to get 1.
\frac{1}{2m-4}+\frac{1}{5n-10}
Express \frac{1}{5n-10}\times 1 as a single fraction.
\frac{1}{2\left(m-2\right)}+\frac{1}{5\left(n-2\right)}
Factor 2m-4. Factor 5n-10.
\frac{5\left(n-2\right)}{10\left(m-2\right)\left(n-2\right)}+\frac{2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(m-2\right) and 5\left(n-2\right) is 10\left(m-2\right)\left(n-2\right). Multiply \frac{1}{2\left(m-2\right)} times \frac{5\left(n-2\right)}{5\left(n-2\right)}. Multiply \frac{1}{5\left(n-2\right)} times \frac{2\left(m-2\right)}{2\left(m-2\right)}.
\frac{5\left(n-2\right)+2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)}
Since \frac{5\left(n-2\right)}{10\left(m-2\right)\left(n-2\right)} and \frac{2\left(m-2\right)}{10\left(m-2\right)\left(n-2\right)} have the same denominator, add them by adding their numerators.
\frac{5n-10+2m-4}{10\left(m-2\right)\left(n-2\right)}
Do the multiplications in 5\left(n-2\right)+2\left(m-2\right).
\frac{5n-14+2m}{10\left(m-2\right)\left(n-2\right)}
Combine like terms in 5n-10+2m-4.
\frac{5n-14+2m}{10mn-20m-20n+40}
Expand 10\left(m-2\right)\left(n-2\right).
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