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Differentiate w.r.t. b
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\frac{2x}{x\left(b+e\right)}+\frac{3y}{ey+by}
Factor the expressions that are not already factored in \frac{2x}{ex+bx}.
\frac{2}{b+e}+\frac{3y}{ey+by}
Cancel out x in both numerator and denominator.
\frac{2}{b+e}+\frac{3y}{y\left(b+e\right)}
Factor the expressions that are not already factored in \frac{3y}{ey+by}.
\frac{2}{b+e}+\frac{3}{b+e}
Cancel out y in both numerator and denominator.
\frac{5}{b+e}
Since \frac{2}{b+e} and \frac{3}{b+e} have the same denominator, add them by adding their numerators. Add 2 and 3 to get 5.