Solve frac{3s^{2}+40s}{s^{3}+4s^2-12s}+5s^2+8s/s^3+4s^2-12s

$$\frac { 3 s ^ { 2 } + 40 s } { s ^ { 3 } + 4 s ^ { 2 } - 12 s } + \frac { 5 s ^ { 2 } + 8 s } { s ^ { 3 } + 4 s ^ { 2 } - 12 s }$$

Evaluate

$$\frac{8}{s-2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3s^{2}+40s}{s^{3}+4s^{2}-12s}.

$$\frac{s\left(3s+40\right)}{s\left(s-2\right)\left(s+6\right)}+\frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}$$

Cancel out s in both numerator and denominator.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}$$

Factor the expressions that are not already factored in \frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{s\left(5s+8\right)}{s\left(s-2\right)\left(s+6\right)}$$

Cancel out s in both numerator and denominator.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{5s+8}{\left(s-2\right)\left(s+6\right)}$$

Since \frac{3s+40}{\left(s-2\right)\left(s+6\right)} and \frac{5s+8}{\left(s-2\right)\left(s+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{3s+40+5s+8}{\left(s-2\right)\left(s+6\right)}$$

Combine like terms in 3s+40+5s+8.

$$\frac{8s+48}{\left(s-2\right)\left(s+6\right)}$$

Factor the expressions that are not already factored in \frac{8s+48}{\left(s-2\right)\left(s+6\right)}.

$$\frac{8\left(s+6\right)}{\left(s-2\right)\left(s+6\right)}$$

Cancel out s+6 in both numerator and denominator.

$$\frac{8}{s-2}$$

Expand

$$\frac{8}{s-2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3s^{2}+40s}{s^{3}+4s^{2}-12s}.

$$\frac{s\left(3s+40\right)}{s\left(s-2\right)\left(s+6\right)}+\frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}$$

Cancel out s in both numerator and denominator.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}$$

Factor the expressions that are not already factored in \frac{5s^{2}+8s}{s^{3}+4s^{2}-12s}.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{s\left(5s+8\right)}{s\left(s-2\right)\left(s+6\right)}$$

Cancel out s in both numerator and denominator.

$$\frac{3s+40}{\left(s-2\right)\left(s+6\right)}+\frac{5s+8}{\left(s-2\right)\left(s+6\right)}$$

Since \frac{3s+40}{\left(s-2\right)\left(s+6\right)} and \frac{5s+8}{\left(s-2\right)\left(s+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{3s+40+5s+8}{\left(s-2\right)\left(s+6\right)}$$

Combine like terms in 3s+40+5s+8.

$$\frac{8s+48}{\left(s-2\right)\left(s+6\right)}$$

Factor the expressions that are not already factored in \frac{8s+48}{\left(s-2\right)\left(s+6\right)}.

$$\frac{8\left(s+6\right)}{\left(s-2\right)\left(s+6\right)}$$

Cancel out s+6 in both numerator and denominator.

$$\frac{8}{s-2}$$