Answer
(a) Yes
(b) No
Work Step by Step
(a) $\frac{x(x+1)}{(x+1)^{2}}=\frac{x(x+1)}{(x+1)(x+1)}=\frac{x}{x+1}$ hence $\frac{x(x+1)}{(x+1)^{2}}=\frac{x}{x+1}$ is true.
(b) $\sqrt (x^{2}+25)$ can not be simplified any further hence $\sqrt (x^{2}+25)\ne x+5$
