## College Algebra (6th Edition)

$\frac{x+4}{(x+5)^{3/2}}$
$(x+5)^{-1/2}-(x+5)^{-3/2}$ The greatest common factor of $(x+5)^{-1/2}-(x+5)^{-3/2}$ is $(x+5)$ with the smaller exponent in the two terms. Thus the greatest common factor is $(x+5)^{-3/2}$ Express each term as the product of greatest common factor and its other factor. $=(x+5)^{1}(x+5)^{-3/2}-(x+5)^{-3/2}$ $[(x+5)^{1}(x+5)^{-3/2}=(x+5)^{-3/2+1}=(x+5)^{-1/2}]$ Factor out the Greatest common factor. $=(x+5)^{-3/2}((x+5)-1)$ $=(x+5)^{-3/2}(x+5-1)$ $=(x+5)^{-3/2}(x+4)$ $=\frac{(x+4)}{(x+5)^{3/2}}$ $[a^{-1/m} = \frac{1}{a^{1/m}}]$