Solve x-4/x+2*2x/x-2

$$\frac { x - 4 } { x + 2 } \cdot \frac { 2 x } { x - 2 }$$

Evaluate

$$\frac{2x\left(x-4\right)}{x^{2}-4}$$

Short Solution Steps

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

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

Use the distributive property to multiply x-4 by 2.

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

Use the distributive property to multiply 2x-8 by x.

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

Consider \left(x+2\right)\left(x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2x^{2}-8x}{x^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2x^{2}-8x}{x^{2}-4}$$

Expand

$$\frac{2\left(x^{2}-4x\right)}{x^{2}-4}$$

Short Solution Steps

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

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

Use the distributive property to multiply x-4 by 2.

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

Use the distributive property to multiply 2x-8 by x.

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

Consider \left(x+2\right)\left(x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2x^{2}-8x}{x^{2}-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2x^{2}-8x}{x^{2}-4}$$