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

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{7}{x^{2}} and \frac{7x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{7}{x^{2}} and \frac{7x}{x^{2}} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{-7x+7}{7x+7}$$

Factor the expressions that are not already factored.

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

Cancel out 7 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{7}{x^{2}} and \frac{7x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{7}{x^{2}} and \frac{7x}{x^{2}} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{-7x+7}{7x+7}$$

Factor the expressions that are not already factored.

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

Cancel out 7 in both numerator and denominator.

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