Solve 3x-24/x^2-64-(x-2)^2/x^2+6x-16

$$\frac { 3 x - 24 } { x ^ { 2 } - 64 } - \frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } + 6 x - 16 }$$

Evaluate

$$\frac{5-x}{x+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-24}{x^{2}-64}.

$$\frac{3\left(x-8\right)}{\left(x-8\right)\left(x+8\right)}-\frac{\left(x-2\right)^{2}}{x^{2}+6x-16}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{3}{x+8}-\frac{\left(x-2\right)^{2}}{x^{2}+6x-16}$$

Factor the expressions that are not already factored in \frac{\left(x-2\right)^{2}}{x^{2}+6x-16}.

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

Cancel out x-2 in both numerator and denominator.

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

Since \frac{3}{x+8} and \frac{x-2}{x+8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-\left(x-2\right)}{x+8}$$

Do the multiplications in 3-\left(x-2\right).

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

Combine like terms in 3-x+2.

$$\frac{5-x}{x+8}$$

Expand

$$\frac{5-x}{x+8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-24}{x^{2}-64}.

$$\frac{3\left(x-8\right)}{\left(x-8\right)\left(x+8\right)}-\frac{\left(x-2\right)^{2}}{x^{2}+6x-16}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{3}{x+8}-\frac{\left(x-2\right)^{2}}{x^{2}+6x-16}$$

Factor the expressions that are not already factored in \frac{\left(x-2\right)^{2}}{x^{2}+6x-16}.

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

Cancel out x-2 in both numerator and denominator.

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

Since \frac{3}{x+8} and \frac{x-2}{x+8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-\left(x-2\right)}{x+8}$$

Do the multiplications in 3-\left(x-2\right).

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

Combine like terms in 3-x+2.

$$\frac{5-x}{x+8}$$