Solve frac{x^{2}-16}{x^{2}-a^{2}}:frac{x^{2}+4x}{x^3-a^2x+x^2-a^2}

$$\frac { x ^ { 2 } - 16 } { x ^ { 2 } - a ^ { 2 } } : \frac { x ^ { 2 } + 4 x } { x ^ { 3 } - a ^ { 2 } x + x ^ { 2 } - a ^ { 2 } }$$

Evaluate

$$x-3-\frac{4}{x}$$

Short Solution Steps

Divide \frac{x^{2}-16}{x^{2}-a^{2}} by \frac{x^{2}+4x}{x^{3}-a^{2}x+x^{2}-a^{2}} by multiplying \frac{x^{2}-16}{x^{2}-a^{2}} by the reciprocal of \frac{x^{2}+4x}{x^{3}-a^{2}x+x^{2}-a^{2}}.

$$\frac{\left(x^{2}-16\right)\left(x^{3}-a^{2}x+x^{2}-a^{2}\right)}{\left(x^{2}-a^{2}\right)\left(x^{2}+4x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-4\right)\left(x+1\right)\left(x+4\right)\left(x+a\right)\left(x-a\right)}{x\left(x+4\right)\left(x+a\right)\left(x-a\right)}$$

Cancel out \left(x+4\right)\left(x+a\right)\left(x-a\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+1\right)}{x}$$

Expand the expression.

$$\frac{x^{2}-3x-4}{x}$$

Expand

$$x-3-\frac{4}{x}$$

Short Solution Steps

Divide \frac{x^{2}-16}{x^{2}-a^{2}} by \frac{x^{2}+4x}{x^{3}-a^{2}x+x^{2}-a^{2}} by multiplying \frac{x^{2}-16}{x^{2}-a^{2}} by the reciprocal of \frac{x^{2}+4x}{x^{3}-a^{2}x+x^{2}-a^{2}}.

$$\frac{\left(x^{2}-16\right)\left(x^{3}-a^{2}x+x^{2}-a^{2}\right)}{\left(x^{2}-a^{2}\right)\left(x^{2}+4x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-4\right)\left(x+1\right)\left(x+4\right)\left(x+a\right)\left(x-a\right)}{x\left(x+4\right)\left(x+a\right)\left(x-a\right)}$$

Cancel out \left(x+4\right)\left(x+a\right)\left(x-a\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+1\right)}{x}$$

Expand the expression.

$$\frac{x^{2}-3x-4}{x}$$