Solve frac{(3a^{2}b-6ab+5b^{2})-(4ab-6b^{2}-5a^{2}b)}{(8r^2-5c^2+2rt)+(-6rt+2t^2-r^2)}

$$\frac { ( 3 a ^ { 2 } b - 6 a b + 5 b ^ { 2 } ) - ( 4 a b - 6 b ^ { 2 } - 5 a ^ { 2 } b ) } { ( 8 r ^ { 2 } - 5 c ^ { 2 } + 2 r t ) + ( - 6 r t + 2 t ^ { 2 } - r ^ { 2 } ) }$$

Evaluate

$$\frac{b\left(8a^{2}+11b-10a\right)}{7r^{2}-4rt+2t^{2}-5c^{2}}$$

$$\left(r\neq \frac{\sqrt{35c^{2}-10t^{2}}+2t}{7}\text{ and }r\neq \frac{-\sqrt{35c^{2}-10t^{2}}+2t}{7}\right)\text{ or }|c|<\frac{\sqrt{14}|t|}{7}$$

Expand

$$\frac{8ba^{2}-10ab+11b^{2}}{7r^{2}-4rt+2t^{2}-5c^{2}}$$

$$\left(r\neq \frac{\sqrt{35c^{2}-10t^{2}}+2t}{7}\text{ and }r\neq \frac{-\sqrt{35c^{2}-10t^{2}}+2t}{7}\right)\text{ or }|c|<\frac{\sqrt{14}|t|}{7}$$