Solve x/6-6/x/frac{x+6{36}}

$$\frac { \frac { x } { 6 } - \frac { 6 } { x } } { \frac { x + 6 } { 36 } }$$

Evaluate

$$6-\frac{36}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and x is 6x. Multiply \frac{x}{6} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{6}{6}.

$$\frac{\frac{xx}{6x}-\frac{6\times 6}{6x}}{\frac{x+6}{36}}$$

Since \frac{xx}{6x} and \frac{6\times 6}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-6\times 6}{6x}}{\frac{x+6}{36}}$$

Do the multiplications in xx-6\times 6.

$$\frac{\frac{x^{2}-36}{6x}}{\frac{x+6}{36}}$$

Divide \frac{x^{2}-36}{6x} by \frac{x+6}{36} by multiplying \frac{x^{2}-36}{6x} by the reciprocal of \frac{x+6}{36}.

$$\frac{\left(x^{2}-36\right)\times 36}{6x\left(x+6\right)}$$

Cancel out 6 in both numerator and denominator.

$$\frac{6\left(x^{2}-36\right)}{x\left(x+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(x-6\right)\left(x+6\right)}{x\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{6\left(x-6\right)}{x}$$

Expand the expression.

$$\frac{6x-36}{x}$$

Expand

$$6-\frac{36}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and x is 6x. Multiply \frac{x}{6} times \frac{x}{x}. Multiply \frac{6}{x} times \frac{6}{6}.

$$\frac{\frac{xx}{6x}-\frac{6\times 6}{6x}}{\frac{x+6}{36}}$$

Since \frac{xx}{6x} and \frac{6\times 6}{6x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-6\times 6}{6x}}{\frac{x+6}{36}}$$

Do the multiplications in xx-6\times 6.

$$\frac{\frac{x^{2}-36}{6x}}{\frac{x+6}{36}}$$

Divide \frac{x^{2}-36}{6x} by \frac{x+6}{36} by multiplying \frac{x^{2}-36}{6x} by the reciprocal of \frac{x+6}{36}.

$$\frac{\left(x^{2}-36\right)\times 36}{6x\left(x+6\right)}$$

Cancel out 6 in both numerator and denominator.

$$\frac{6\left(x^{2}-36\right)}{x\left(x+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(x-6\right)\left(x+6\right)}{x\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{6\left(x-6\right)}{x}$$

Expand the expression.

$$\frac{6x-36}{x}$$