Solve 14s^2/s^2-8s+15*(s^2-a)div(2s^2+6s)

$$\frac { 14 s ^ { 2 } } { s ^ { 2 } - 8 s + 15 } \times ( s ^ { 2 } - a ) \div ( 2 s ^ { 2 } + 6 s )$$

Evaluate

$$\frac{7s\left(s^{2}-a\right)}{\left(s-5\right)\left(s^{2}-9\right)}$$

Short Solution Steps

Express \frac{14s^{2}}{s^{2}-8s+15}\left(s^{2}-a\right) as a single fraction.

$$\frac{\frac{14s^{2}\left(s^{2}-a\right)}{s^{2}-8s+15}}{2s^{2}+6s}$$

Express \frac{\frac{14s^{2}\left(s^{2}-a\right)}{s^{2}-8s+15}}{2s^{2}+6s} as a single fraction.

$$\frac{14s^{2}\left(s^{2}-a\right)}{\left(s^{2}-8s+15\right)\left(2s^{2}+6s\right)}$$

Factor the expressions that are not already factored.

$$\frac{14s^{2}\left(s^{2}-a\right)}{2s\left(s-5\right)\left(s-3\right)\left(s+3\right)}$$

Cancel out 2s in both numerator and denominator.

$$\frac{7s\left(s^{2}-a\right)}{\left(s-5\right)\left(s-3\right)\left(s+3\right)}$$

Expand the expression.

$$\frac{7s^{3}-7as}{s^{3}-5s^{2}-9s+45}$$

Expand

$$-\frac{7\left(as-s^{3}\right)}{\left(s+3\right)\left(s^{2}-8s+15\right)}$$

Short Solution Steps

Express \frac{14s^{2}}{s^{2}-8s+15}\left(s^{2}-a\right) as a single fraction.

$$\frac{\frac{14s^{2}\left(s^{2}-a\right)}{s^{2}-8s+15}}{2s^{2}+6s}$$

Express \frac{\frac{14s^{2}\left(s^{2}-a\right)}{s^{2}-8s+15}}{2s^{2}+6s} as a single fraction.

$$\frac{14s^{2}\left(s^{2}-a\right)}{\left(s^{2}-8s+15\right)\left(2s^{2}+6s\right)}$$

Factor the expressions that are not already factored.

$$\frac{14s^{2}\left(s^{2}-a\right)}{2s\left(s-5\right)\left(s-3\right)\left(s+3\right)}$$

Cancel out 2s in both numerator and denominator.

$$\frac{7s\left(s^{2}-a\right)}{\left(s-5\right)\left(s-3\right)\left(s+3\right)}$$

Expand the expression.

$$\frac{7s^{3}-7as}{s^{3}-5s^{2}-9s+45}$$