Solve x^2-64/8x-40+x^2+16x+64/x^2+3x-40

$$\frac { x ^ { 2 } - 64 } { 8 x - 40 } + \frac { x ^ { 2 } + 16 x + 64 } { x ^ { 2 } + 3 x - 40 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+16x+64}{x^{2}+3x-40}.

$$\frac{x^{2}-64}{8x-40}+\frac{\left(x+8\right)^{2}}{\left(x-5\right)\left(x+8\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x^{2}-64}{8x-40}+\frac{x+8}{x-5}$$

Factor 8x-40.

$$\frac{x^{2}-64}{8\left(x-5\right)}+\frac{x+8}{x-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8\left(x-5\right) and x-5 is 8\left(x-5\right). Multiply \frac{x+8}{x-5} times \frac{8}{8}.

$$\frac{x^{2}-64}{8\left(x-5\right)}+\frac{8\left(x+8\right)}{8\left(x-5\right)}$$

Since \frac{x^{2}-64}{8\left(x-5\right)} and \frac{8\left(x+8\right)}{8\left(x-5\right)} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-64+8\left(x+8\right)}{8\left(x-5\right)}$$

Do the multiplications in x^{2}-64+8\left(x+8\right).

$$\frac{x^{2}-64+8x+64}{8\left(x-5\right)}$$

Combine like terms in x^{2}-64+8x+64.

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

Expand 8\left(x-5\right).

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+16x+64}{x^{2}+3x-40}.

$$\frac{x^{2}-64}{8x-40}+\frac{\left(x+8\right)^{2}}{\left(x-5\right)\left(x+8\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x^{2}-64}{8x-40}+\frac{x+8}{x-5}$$

Factor 8x-40.

$$\frac{x^{2}-64}{8\left(x-5\right)}+\frac{x+8}{x-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8\left(x-5\right) and x-5 is 8\left(x-5\right). Multiply \frac{x+8}{x-5} times \frac{8}{8}.

$$\frac{x^{2}-64}{8\left(x-5\right)}+\frac{8\left(x+8\right)}{8\left(x-5\right)}$$

Since \frac{x^{2}-64}{8\left(x-5\right)} and \frac{8\left(x+8\right)}{8\left(x-5\right)} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}-64+8\left(x+8\right)}{8\left(x-5\right)}$$

Do the multiplications in x^{2}-64+8\left(x+8\right).

$$\frac{x^{2}-64+8x+64}{8\left(x-5\right)}$$

Combine like terms in x^{2}-64+8x+64.

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

Expand 8\left(x-5\right).

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