Solve 1+7/x-8/x^2/1+frac{8{x}}

$$\frac { 1 + \frac { 7 } { x } - \frac { 8 } { x ^ { 2 } } } { 1 + \frac { 8 } { x } }$$

Evaluate

$$\frac{x-1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}+\frac{7}{x}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

Since \frac{x}{x} and \frac{7}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+7}{x}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x+7}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x+7\right)x}{x^{2}}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

Since \frac{\left(x+7\right)x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x+7\right)x-8}{x^{2}}}{1+\frac{8}{x}}$$

Do the multiplications in \left(x+7\right)x-8.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{1+\frac{8}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{\frac{x}{x}+\frac{8}{x}}$$

Since \frac{x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{\frac{x+8}{x}}$$

Divide \frac{x^{2}+7x-8}{x^{2}} by \frac{x+8}{x} by multiplying \frac{x^{2}+7x-8}{x^{2}} by the reciprocal of \frac{x+8}{x}.

$$\frac{\left(x^{2}+7x-8\right)x}{x^{2}\left(x+8\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+7x-8}{x\left(x+8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+8\right)}{x\left(x+8\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x-1}{x}$$

Expand

$$\frac{x-1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}+\frac{7}{x}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

Since \frac{x}{x} and \frac{7}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+7}{x}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x+7}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x+7\right)x}{x^{2}}-\frac{8}{x^{2}}}{1+\frac{8}{x}}$$

Since \frac{\left(x+7\right)x}{x^{2}} and \frac{8}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x+7\right)x-8}{x^{2}}}{1+\frac{8}{x}}$$

Do the multiplications in \left(x+7\right)x-8.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{1+\frac{8}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{\frac{x}{x}+\frac{8}{x}}$$

Since \frac{x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+7x-8}{x^{2}}}{\frac{x+8}{x}}$$

Divide \frac{x^{2}+7x-8}{x^{2}} by \frac{x+8}{x} by multiplying \frac{x^{2}+7x-8}{x^{2}} by the reciprocal of \frac{x+8}{x}.

$$\frac{\left(x^{2}+7x-8\right)x}{x^{2}\left(x+8\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+7x-8}{x\left(x+8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)\left(x+8\right)}{x\left(x+8\right)}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x-1}{x}$$