Simplify ((a^2+b)^(3/2))/(a^2+b)

$\frac{{(a^{2} + b)}^{\frac{3}{2}}}{a^{2} + b}$

Factor $a^{2} + b$ out of ${(a^{2} + b)}^{\frac{3}{2}}$ .

$\frac{(a^{2} + b) {(a^{2} + b)}^{\frac{1}{2}}}{a^{2} + b}$

Cancel the common factors.

Multiply by $1$ .

$\frac{(a^{2} + b) {(a^{2} + b)}^{\frac{1}{2}}}{(a^{2} + b) \cdot 1}$

Cancel the common factor.

$\frac{(a^{2} + b) {(a^{2} + b)}^{\frac{1}{2}}}{(a^{2} + b) \cdot 1}$

Rewrite the expression.

$\frac{{(a^{2} + b)}^{\frac{1}{2}}}{1}$

Divide ${(a^{2} + b)}^{\frac{1}{2}}$ by $1$ .

${(a^{2} + b)}^{\frac{1}{2}}$