Solve x-6/x-x-9/4

$$\frac { x - 6 } { x } - \frac { x - 9 } { 4 }$$

Evaluate

$$-\frac{x}{4}+\frac{13}{4}-\frac{6}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 4 is 4x. Multiply \frac{x-6}{x} times \frac{4}{4}. Multiply \frac{x-9}{4} times \frac{x}{x}.

$$\frac{4\left(x-6\right)}{4x}-\frac{\left(x-9\right)x}{4x}$$

Since \frac{4\left(x-6\right)}{4x} and \frac{\left(x-9\right)x}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x-6\right)-\left(x-9\right)x}{4x}$$

Do the multiplications in 4\left(x-6\right)-\left(x-9\right)x.

$$\frac{4x-24-x^{2}+9x}{4x}$$

Combine like terms in 4x-24-x^{2}+9x.

$$\frac{13x-24-x^{2}}{4x}$$

Expand

$$-\frac{x}{4}+\frac{13}{4}-\frac{6}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 4 is 4x. Multiply \frac{x-6}{x} times \frac{4}{4}. Multiply \frac{x-9}{4} times \frac{x}{x}.

$$\frac{4\left(x-6\right)}{4x}-\frac{\left(x-9\right)x}{4x}$$

Since \frac{4\left(x-6\right)}{4x} and \frac{\left(x-9\right)x}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x-6\right)-\left(x-9\right)x}{4x}$$

Do the multiplications in 4\left(x-6\right)-\left(x-9\right)x.

$$\frac{4x-24-x^{2}+9x}{4x}$$

Combine like terms in 4x-24-x^{2}+9x.

$$\frac{13x-24-x^{2}}{4x}$$