Solve 1+2/x-15/x^2/1+frac{4{x}-5/x^2}

$$\frac { 1 + \frac { 2 } { x } - \frac { 15 } { x ^ { 2 } } } { 1 + \frac { 4 } { x } - \frac { 5 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x-3}{x-1}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{2}{x}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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

$$\frac{\frac{x+2}{x}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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+2}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x+2\right)x}{x^{2}}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

Since \frac{\left(x+2\right)x}{x^{2}} and \frac{15}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x+2\right)x-15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

Do the multiplications in \left(x+2\right)x-15.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x}{x}+\frac{4}{x}-\frac{5}{x^{2}}}$$

Since \frac{x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x+4}{x}-\frac{5}{x^{2}}}$$

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+4}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{\left(x+4\right)x}{x^{2}}-\frac{5}{x^{2}}}$$

Since \frac{\left(x+4\right)x}{x^{2}} and \frac{5}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{\left(x+4\right)x-5}{x^{2}}}$$

Do the multiplications in \left(x+4\right)x-5.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x^{2}+4x-5}{x^{2}}}$$

Divide \frac{x^{2}+2x-15}{x^{2}} by \frac{x^{2}+4x-5}{x^{2}} by multiplying \frac{x^{2}+2x-15}{x^{2}} by the reciprocal of \frac{x^{2}+4x-5}{x^{2}}.

$$\frac{\left(x^{2}+2x-15\right)x^{2}}{x^{2}\left(x^{2}+4x-5\right)}$$

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

$$\frac{x^{2}+2x-15}{x^{2}+4x-5}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-3}{x-1}$$

Expand

$$\frac{x-3}{x-1}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}+\frac{2}{x}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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

$$\frac{\frac{x+2}{x}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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+2}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x+2\right)x}{x^{2}}-\frac{15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

Since \frac{\left(x+2\right)x}{x^{2}} and \frac{15}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x+2\right)x-15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

Do the multiplications in \left(x+2\right)x-15.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{1+\frac{4}{x}-\frac{5}{x^{2}}}$$

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

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x}{x}+\frac{4}{x}-\frac{5}{x^{2}}}$$

Since \frac{x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x+4}{x}-\frac{5}{x^{2}}}$$

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+4}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{\left(x+4\right)x}{x^{2}}-\frac{5}{x^{2}}}$$

Since \frac{\left(x+4\right)x}{x^{2}} and \frac{5}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{\left(x+4\right)x-5}{x^{2}}}$$

Do the multiplications in \left(x+4\right)x-5.

$$\frac{\frac{x^{2}+2x-15}{x^{2}}}{\frac{x^{2}+4x-5}{x^{2}}}$$

Divide \frac{x^{2}+2x-15}{x^{2}} by \frac{x^{2}+4x-5}{x^{2}} by multiplying \frac{x^{2}+2x-15}{x^{2}} by the reciprocal of \frac{x^{2}+4x-5}{x^{2}}.

$$\frac{\left(x^{2}+2x-15\right)x^{2}}{x^{2}\left(x^{2}+4x-5\right)}$$

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

$$\frac{x^{2}+2x-15}{x^{2}+4x-5}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-3}{x-1}$$