Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set - Page 516: 42

$\dfrac{5}{(x+1)(x+5)}-\dfrac{2}{(x+5)^{2}}=\dfrac{3x+23}{(x+5)^{2}(x+1)}$

$\dfrac{5}{(x+1)(x+5)}-\dfrac{2}{(x+5)^{2}}$ Evaluate the substraction of the two rational expressions and simplify: $\dfrac{5}{(x+1)(x+5)}-\dfrac{2}{(x+5)^{2}}=\dfrac{5(x+5)-2(x+1)}{(x+5)^{2}(x+1)}=...$ $...=\dfrac{5x+25-2x-2}{(x+5)^{2}(x+1)}=\dfrac{3x+23}{(x+5)^{2}(x+1)}$