Solve 1-5/x-14/x^2/1+frac{7{x}+10/x^2}

$$\frac { 1 - \frac { 5 } { x } - \frac { 14 } { x ^ { 2 } } } { 1 + \frac { 7 } { x } + \frac { 10 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x-7}{x+5}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{5}{x}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Since \frac{x}{x} and \frac{5}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{x}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

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-5}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-5\right)x}{x^{2}}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Since \frac{\left(x-5\right)x}{x^{2}} and \frac{14}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-5\right)x-14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Do the multiplications in \left(x-5\right)x-14.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x}{x}+\frac{7}{x}+\frac{10}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x+7}{x}+\frac{10}{x^{2}}}$$

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}.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{\left(x+7\right)x}{x^{2}}+\frac{10}{x^{2}}}$$

Since \frac{\left(x+7\right)x}{x^{2}} and \frac{10}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{\left(x+7\right)x+10}{x^{2}}}$$

Do the multiplications in \left(x+7\right)x+10.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x^{2}+7x+10}{x^{2}}}$$

Divide \frac{x^{2}-5x-14}{x^{2}} by \frac{x^{2}+7x+10}{x^{2}} by multiplying \frac{x^{2}-5x-14}{x^{2}} by the reciprocal of \frac{x^{2}+7x+10}{x^{2}}.

$$\frac{\left(x^{2}-5x-14\right)x^{2}}{x^{2}\left(x^{2}+7x+10\right)}$$

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

$$\frac{x^{2}-5x-14}{x^{2}+7x+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-7}{x+5}$$

Expand

$$\frac{x-7}{x+5}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{5}{x}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Since \frac{x}{x} and \frac{5}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{x}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

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-5}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-5\right)x}{x^{2}}-\frac{14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Since \frac{\left(x-5\right)x}{x^{2}} and \frac{14}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-5\right)x-14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

Do the multiplications in \left(x-5\right)x-14.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{1+\frac{7}{x}+\frac{10}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x}{x}+\frac{7}{x}+\frac{10}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x+7}{x}+\frac{10}{x^{2}}}$$

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}.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{\left(x+7\right)x}{x^{2}}+\frac{10}{x^{2}}}$$

Since \frac{\left(x+7\right)x}{x^{2}} and \frac{10}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{\left(x+7\right)x+10}{x^{2}}}$$

Do the multiplications in \left(x+7\right)x+10.

$$\frac{\frac{x^{2}-5x-14}{x^{2}}}{\frac{x^{2}+7x+10}{x^{2}}}$$

Divide \frac{x^{2}-5x-14}{x^{2}} by \frac{x^{2}+7x+10}{x^{2}} by multiplying \frac{x^{2}-5x-14}{x^{2}} by the reciprocal of \frac{x^{2}+7x+10}{x^{2}}.

$$\frac{\left(x^{2}-5x-14\right)x^{2}}{x^{2}\left(x^{2}+7x+10\right)}$$

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

$$\frac{x^{2}-5x-14}{x^{2}+7x+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+2\right)}{\left(x+2\right)\left(x+5\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-7}{x+5}$$