Evaluate
\frac{3x+16}{10\left(x+3\right)}
Expand
\frac{3x+16}{10\left(x+3\right)}
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\frac{x+2}{2\left(x+3\right)}-\frac{x-3}{5\left(x+3\right)}
Factor 2x+6. Factor 5x+15.
\frac{5\left(x+2\right)}{10\left(x+3\right)}-\frac{2\left(x-3\right)}{10\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+3\right) and 5\left(x+3\right) is 10\left(x+3\right). Multiply \frac{x+2}{2\left(x+3\right)} times \frac{5}{5}. Multiply \frac{x-3}{5\left(x+3\right)} times \frac{2}{2}.
\frac{5\left(x+2\right)-2\left(x-3\right)}{10\left(x+3\right)}
Since \frac{5\left(x+2\right)}{10\left(x+3\right)} and \frac{2\left(x-3\right)}{10\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+10-2x+6}{10\left(x+3\right)}
Do the multiplications in 5\left(x+2\right)-2\left(x-3\right).
\frac{3x+16}{10\left(x+3\right)}
Combine like terms in 5x+10-2x+6.
\frac{3x+16}{10x+30}
Expand 10\left(x+3\right).
\frac{x+2}{2\left(x+3\right)}-\frac{x-3}{5\left(x+3\right)}
Factor 2x+6. Factor 5x+15.
\frac{5\left(x+2\right)}{10\left(x+3\right)}-\frac{2\left(x-3\right)}{10\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+3\right) and 5\left(x+3\right) is 10\left(x+3\right). Multiply \frac{x+2}{2\left(x+3\right)} times \frac{5}{5}. Multiply \frac{x-3}{5\left(x+3\right)} times \frac{2}{2}.
\frac{5\left(x+2\right)-2\left(x-3\right)}{10\left(x+3\right)}
Since \frac{5\left(x+2\right)}{10\left(x+3\right)} and \frac{2\left(x-3\right)}{10\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{5x+10-2x+6}{10\left(x+3\right)}
Do the multiplications in 5\left(x+2\right)-2\left(x-3\right).
\frac{3x+16}{10\left(x+3\right)}
Combine like terms in 5x+10-2x+6.
\frac{3x+16}{10x+30}
Expand 10\left(x+3\right).
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Differentiation
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Limits
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