Solve sin+10/m^2-m-2divm^2-4/3m+3

$$\frac { \sin + 10 } { m ^ { 2 } - m - 2 } \div \frac { m ^ { 2 } - 4 } { 3 m + 3 }$$

Evaluate

$$\frac{52094453300079099}{100000000000000000\left(m+2\right)\left(m-2\right)^{2}}$$

Short Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.17364817766693033}{m ^ {2} - m - 2} / \frac{m ^ {2} - 4}{3 m + 3}$$

Divide \frac{0.17364817766693033}{m^{2}-m-2} by \frac{m^{2}-4}{3m+3} by multiplying \frac{0.17364817766693033}{m^{2}-m-2} by the reciprocal of \frac{m^{2}-4}{3m+3}.

$$\frac{0.17364817766693033\left(3m+3\right)}{\left(m^{2}-m-2\right)\left(m^{2}-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{0.17364817766693033\times 3\left(m+1\right)}{\left(m+1\right)\left(m+2\right)\left(m-2\right)^{2}}$$

Cancel out m+1 in both numerator and denominator.

$$\frac{0.17364817766693033\times 3}{\left(m+2\right)\left(m-2\right)^{2}}$$

Expand the expression.

$$\frac{0.52094453300079099}{m^{3}-2m^{2}-4m+8}$$

Expand

$$\frac{52094453300079099}{100000000000000000\left(m-2\right)\left(m^{2}-4\right)}$$

Short Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.17364817766693033}{m ^ {2} - m - 2} / \frac{m ^ {2} - 4}{3 m + 3}$$

Divide \frac{0.17364817766693033}{m^{2}-m-2} by \frac{m^{2}-4}{3m+3} by multiplying \frac{0.17364817766693033}{m^{2}-m-2} by the reciprocal of \frac{m^{2}-4}{3m+3}.

$$\frac{0.17364817766693033\left(3m+3\right)}{\left(m^{2}-m-2\right)\left(m^{2}-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{0.17364817766693033\times 3\left(m+1\right)}{\left(m+1\right)\left(m+2\right)\left(m-2\right)^{2}}$$

Cancel out m+1 in both numerator and denominator.

$$\frac{0.17364817766693033\times 3}{\left(m+2\right)\left(m-2\right)^{2}}$$

Expand the expression.

$$\frac{0.52094453300079099}{m^{3}-2m^{2}-4m+8}$$