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Differentiate w.r.t. d
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\frac{8}{d-8}+\frac{5\left(-1\right)}{d-8}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of d-8 and 8-d is d-8. Multiply \frac{5}{8-d} times \frac{-1}{-1}.
\frac{8+5\left(-1\right)}{d-8}
Since \frac{8}{d-8} and \frac{5\left(-1\right)}{d-8} have the same denominator, add them by adding their numerators.
\frac{8-5}{d-8}
Do the multiplications in 8+5\left(-1\right).
\frac{3}{d-8}
Do the calculations in 8-5.