Solve 2(4-x)-2x(4-x)div(4-x^2

$$2(4-x)-2x(4-x) \div (4- { x }^{ 2 }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Factor 4-x^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 8-2x times \frac{\left(x-2\right)\left(-x-2\right)}{\left(x-2\right)\left(-x-2\right)}.

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

Since \frac{\left(8-2x\right)\left(x-2\right)\left(-x-2\right)}{\left(x-2\right)\left(-x-2\right)} and \frac{8x-2x^{2}}{\left(x-2\right)\left(-x-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(8-2x\right)\left(x-2\right)\left(-x-2\right)-\left(8x-2x^{2}\right).

$$\frac{-8x^{2}+32+2x^{3}-8x-8x+2x^{2}}{\left(x-2\right)\left(-x-2\right)}$$

Combine like terms in -8x^{2}+32+2x^{3}-8x-8x+2x^{2}.

$$\frac{-6x^{2}+32+2x^{3}-16x}{\left(x-2\right)\left(-x-2\right)}$$

Expand \left(x-2\right)\left(-x-2\right).

$$\frac{-6x^{2}+32+2x^{3}-16x}{-x^{2}+4}$$

Expand

$$\frac{2\left(x^{3}-3x^{2}-8x+16\right)}{4-x^{2}}$$

Short Solution Steps

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

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

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

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

Factor 4-x^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 8-2x times \frac{\left(x-2\right)\left(-x-2\right)}{\left(x-2\right)\left(-x-2\right)}.

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

Since \frac{\left(8-2x\right)\left(x-2\right)\left(-x-2\right)}{\left(x-2\right)\left(-x-2\right)} and \frac{8x-2x^{2}}{\left(x-2\right)\left(-x-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(8-2x\right)\left(x-2\right)\left(-x-2\right)-\left(8x-2x^{2}\right).

$$\frac{-8x^{2}+32+2x^{3}-8x-8x+2x^{2}}{\left(x-2\right)\left(-x-2\right)}$$

Combine like terms in -8x^{2}+32+2x^{3}-8x-8x+2x^{2}.

$$\frac{-6x^{2}+32+2x^{3}-16x}{\left(x-2\right)\left(-x-2\right)}$$

Expand \left(x-2\right)\left(-x-2\right).

$$\frac{-6x^{2}+32+2x^{3}-16x}{-x^{2}+4}$$