Solve g(x)=x^3+8x/x^2-64divx^2+4x-45/x^2+x-72

$$g ( x ) = \frac { x ^ { 3 } + 8 x } { x ^ { 2 } - 64 } \div \frac { x ^ { 2 } + 4 x - 45 } { x ^ { 2 } + x - 72 }$$

Evaluate

$$\frac{x\left(x^{2}+8\right)}{\left(x-5\right)\left(x+8\right)}$$

Short Solution Steps

Divide \frac{x^{3}+8x}{x^{2}-64} by \frac{x^{2}+4x-45}{x^{2}+x-72} by multiplying \frac{x^{3}+8x}{x^{2}-64} by the reciprocal of \frac{x^{2}+4x-45}{x^{2}+x-72}.

$$\frac{\left(x^{3}+8x\right)\left(x^{2}+x-72\right)}{\left(x^{2}-64\right)\left(x^{2}+4x-45\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-8\right)\left(x+9\right)\left(x^{2}+8\right)}{\left(x-8\right)\left(x-5\right)\left(x+8\right)\left(x+9\right)}$$

Cancel out \left(x-8\right)\left(x+9\right) in both numerator and denominator.

$$\frac{x\left(x^{2}+8\right)}{\left(x-5\right)\left(x+8\right)}$$

Expand the expression.

$$\frac{x^{3}+8x}{x^{2}+3x-40}$$

Expand

$$\frac{x^{3}+8x}{\left(x-5\right)\left(x+8\right)}$$

Short Solution Steps

Divide \frac{x^{3}+8x}{x^{2}-64} by \frac{x^{2}+4x-45}{x^{2}+x-72} by multiplying \frac{x^{3}+8x}{x^{2}-64} by the reciprocal of \frac{x^{2}+4x-45}{x^{2}+x-72}.

$$\frac{\left(x^{3}+8x\right)\left(x^{2}+x-72\right)}{\left(x^{2}-64\right)\left(x^{2}+4x-45\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-8\right)\left(x+9\right)\left(x^{2}+8\right)}{\left(x-8\right)\left(x-5\right)\left(x+8\right)\left(x+9\right)}$$

Cancel out \left(x-8\right)\left(x+9\right) in both numerator and denominator.

$$\frac{x\left(x^{2}+8\right)}{\left(x-5\right)\left(x+8\right)}$$

Expand the expression.

$$\frac{x^{3}+8x}{x^{2}+3x-40}$$