Solve 1-13/x+36/x^2/1-frac{16{x}+63/x^2}

$$\frac { 1 - \frac { 13 } { x } + \frac { 36 } { x ^ { 2 } } } { 1 - \frac { 16 } { x } + \frac { 63 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x-4}{x-7}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{13}{x}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{x}{x} and \frac{13}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-13}{x}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

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-13}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-13\right)x}{x^{2}}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{\left(x-13\right)x}{x^{2}} and \frac{36}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(x-13\right)x+36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Do the multiplications in \left(x-13\right)x+36.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x}{x}-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{x}{x} and \frac{16}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x-16}{x}+\frac{63}{x^{2}}}$$

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-16}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{\left(x-16\right)x}{x^{2}}+\frac{63}{x^{2}}}$$

Since \frac{\left(x-16\right)x}{x^{2}} and \frac{63}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{\left(x-16\right)x+63}{x^{2}}}$$

Do the multiplications in \left(x-16\right)x+63.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x^{2}-16x+63}{x^{2}}}$$

Divide \frac{x^{2}-13x+36}{x^{2}} by \frac{x^{2}-16x+63}{x^{2}} by multiplying \frac{x^{2}-13x+36}{x^{2}} by the reciprocal of \frac{x^{2}-16x+63}{x^{2}}.

$$\frac{\left(x^{2}-13x+36\right)x^{2}}{x^{2}\left(x^{2}-16x+63\right)}$$

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

$$\frac{x^{2}-13x+36}{x^{2}-16x+63}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-4\right)}{\left(x-9\right)\left(x-7\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x-4}{x-7}$$

Expand

$$\frac{x-4}{x-7}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{13}{x}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{x}{x} and \frac{13}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-13}{x}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

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-13}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-13\right)x}{x^{2}}+\frac{36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{\left(x-13\right)x}{x^{2}} and \frac{36}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(x-13\right)x+36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

Do the multiplications in \left(x-13\right)x+36.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{1-\frac{16}{x}+\frac{63}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x}{x}-\frac{16}{x}+\frac{63}{x^{2}}}$$

Since \frac{x}{x} and \frac{16}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x-16}{x}+\frac{63}{x^{2}}}$$

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-16}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{\left(x-16\right)x}{x^{2}}+\frac{63}{x^{2}}}$$

Since \frac{\left(x-16\right)x}{x^{2}} and \frac{63}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{\left(x-16\right)x+63}{x^{2}}}$$

Do the multiplications in \left(x-16\right)x+63.

$$\frac{\frac{x^{2}-13x+36}{x^{2}}}{\frac{x^{2}-16x+63}{x^{2}}}$$

Divide \frac{x^{2}-13x+36}{x^{2}} by \frac{x^{2}-16x+63}{x^{2}} by multiplying \frac{x^{2}-13x+36}{x^{2}} by the reciprocal of \frac{x^{2}-16x+63}{x^{2}}.

$$\frac{\left(x^{2}-13x+36\right)x^{2}}{x^{2}\left(x^{2}-16x+63\right)}$$

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

$$\frac{x^{2}-13x+36}{x^{2}-16x+63}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-4\right)}{\left(x-9\right)\left(x-7\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{x-4}{x-7}$$