# Factoring exponents that differ by an integer

The "last two steps" are just combining like terms. The derivative of $x(x+ 3)^{1/2}$ is, as you say, $(x+ 3)^{1/2}+ (1/2)x(x+ 3)^{-1/2}$. You can, then, factor $(x+ 3)^{-1/2}$. Of course, $(x+ 3)^{1/2}= (x+ 3)(x+ 3)^{-1/2}$ so that gives $(x+ 3)^{-1/2}(x+ 3- (1/2)x)$. That denominator that was cut off should be a 2, not a 3. And x- (1/2)x= (1/2)x so that is equal to $(x+ 3)^{-1/2}((1/2)x+ 3)$