Solve x-4/x+2*2+x/3-xdivx-8/x-3

$$\frac { x - 4 } { x + 2 } \cdot \frac { 2 + x } { 3 - x } \div \frac { x - 8 } { x - 3 }$$

Evaluate

$$-\frac{x-4}{x-8}$$

Solution Steps

Multiply \frac{x-4}{x+2} times \frac{2+x}{3-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x-4\right)\left(2+x\right)}{\left(x+2\right)\left(3-x\right)}}{\frac{x-8}{x-3}}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{\frac{x-4}{-x+3}}{\frac{x-8}{x-3}}$$

Divide \frac{x-4}{-x+3} by \frac{x-8}{x-3} by multiplying \frac{x-4}{-x+3} by the reciprocal of \frac{x-8}{x-3}.

$$\frac{\left(x-4\right)\left(x-3\right)}{\left(-x+3\right)\left(x-8\right)}$$

Extract the negative sign in x-3.

$$\frac{-\left(x-4\right)\left(-x+3\right)}{\left(x-8\right)\left(-x+3\right)}$$

Cancel out -x+3 in both numerator and denominator.

$$\frac{-\left(x-4\right)}{x-8}$$

To find the opposite of x-4, find the opposite of each term.

$$\frac{-x-\left(-4\right)}{x-8}$$

The opposite of -4 is 4.

$$\frac{-x+4}{x-8}$$

Expand

$$-\frac{x-4}{x-8}$$

Solution Steps

Multiply \frac{x-4}{x+2} times \frac{2+x}{3-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x-4\right)\left(2+x\right)}{\left(x+2\right)\left(3-x\right)}}{\frac{x-8}{x-3}}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{\frac{x-4}{-x+3}}{\frac{x-8}{x-3}}$$

Divide \frac{x-4}{-x+3} by \frac{x-8}{x-3} by multiplying \frac{x-4}{-x+3} by the reciprocal of \frac{x-8}{x-3}.

$$\frac{\left(x-4\right)\left(x-3\right)}{\left(-x+3\right)\left(x-8\right)}$$

Extract the negative sign in x-3.

$$\frac{-\left(x-4\right)\left(-x+3\right)}{\left(x-8\right)\left(-x+3\right)}$$

Cancel out -x+3 in both numerator and denominator.

$$\frac{-\left(x-4\right)}{x-8}$$

To find the opposite of x-4, find the opposite of each term.

$$\frac{-x-\left(-4\right)}{x-8}$$

The opposite of -4 is 4.

$$\frac{-x+4}{x-8}$$