Answer
$\frac{2}{3}(x+3) ; x \ne 3,-3,-\sqrt \frac{5}{ 2}$
Work Step by Step
$\frac{4x^{2}+10}{x-3} \div \frac{6x^{2}+15}{(x^{2}-9)}$
Factorize the numerator and denominators.
$=\frac{2(2x^{2}+5)}{x-3} \div \frac{3(2x^{2}+5)}{(x+3)(x-3)}$
Invert the divisor and multiply. For non-zero denominators, exclude the numbers 3,-3 and $-\sqrt \frac{5}{ 2}$ for $x$.
$=\frac{2(2x^{2}+5)}{x-3} \times \frac{(x+3)(x-3)}{3(2x^{2}+5)}; x \ne 3,-3, -\sqrt \frac{5}{ 2};$
Divide out common factors.
$=\frac{2}{3}(x+3) ; x \ne 3,-3,-\sqrt \frac{5}{ 2}$
