Solve f(x)=x+5/1-frac{x{x-2}}

$$f ( x ) = \frac { x + 5 } { 1 - \frac { x } { x - 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.

$$\frac{x+5}{\frac{x-2}{x-2}-\frac{x}{x-2}}$$

Since \frac{x-2}{x-2} and \frac{x}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+5}{\frac{x-2-x}{x-2}}$$

Combine like terms in x-2-x.

$$\frac{x+5}{\frac{-2}{x-2}}$$

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

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

Apply the distributive property by multiplying each term of x+5 by each term of x-2.

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

Combine -2x and 5x to get 3x.

$$\frac{x^{2}+3x-10}{-2}$$

Expand

$$-\frac{x^{2}}{2}-\frac{3x}{2}+5$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-2}{x-2}.

$$\frac{x+5}{\frac{x-2}{x-2}-\frac{x}{x-2}}$$

Since \frac{x-2}{x-2} and \frac{x}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+5}{\frac{x-2-x}{x-2}}$$

Combine like terms in x-2-x.

$$\frac{x+5}{\frac{-2}{x-2}}$$

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

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

Apply the distributive property by multiplying each term of x+5 by each term of x-2.

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

Combine -2x and 5x to get 3x.

$$\frac{x^{2}+3x-10}{-2}$$