Solve a^2+2ab+8^2/(x-2)^2-x^2+4x-4=

$$\frac { a ^ { 2 } + 2 a b + 8 ^ { 2 } } { ( x - 2 ) ^ { 2 } } - x ^ { 2 } + 4 x - 4 =$$

Evaluate

$$\frac{-\left(x-2\right)^{4}+2ab+a^{2}+64}{\left(x-2\right)^{2}}$$

Short Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\frac{a^{2}+2ab+64}{\left(x-2\right)^{2}}-x^{2}+4x-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -x^{2}+4x-4 times \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{2}}.

$$\frac{a^{2}+2ab+64}{\left(x-2\right)^{2}}+\frac{\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}}$$

Since \frac{a^{2}+2ab+64}{\left(x-2\right)^{2}} and \frac{\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+2ab+64+\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}}$$

Do the multiplications in a^{2}+2ab+64+\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}.

$$\frac{a^{2}+2ab+64-x^{4}+4x^{3}-4x^{2}+4x^{3}-16x^{2}+16x-4x^{2}+16x-16}{\left(x-2\right)^{2}}$$

Combine like terms in a^{2}+2ab+64-x^{4}+4x^{3}-4x^{2}+4x^{3}-16x^{2}+16x-4x^{2}+16x-16.

$$\frac{a^{2}+2ab-24x^{2}+48-x^{4}+8x^{3}+32x}{\left(x-2\right)^{2}}$$

Expand \left(x-2\right)^{2}.

$$\frac{a^{2}+2ab-24x^{2}+48-x^{4}+8x^{3}+32x}{x^{2}-4x+4}$$

Expand

$$\frac{48+a^{2}+2ab+32x-24x^{2}+8x^{3}-x^{4}}{\left(x-2\right)^{2}}$$

Short Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\frac{a^{2}+2ab+64}{\left(x-2\right)^{2}}-x^{2}+4x-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -x^{2}+4x-4 times \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{2}}.

$$\frac{a^{2}+2ab+64}{\left(x-2\right)^{2}}+\frac{\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}}$$

Since \frac{a^{2}+2ab+64}{\left(x-2\right)^{2}} and \frac{\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{a^{2}+2ab+64+\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}}{\left(x-2\right)^{2}}$$

Do the multiplications in a^{2}+2ab+64+\left(-x^{2}+4x-4\right)\left(x-2\right)^{2}.

$$\frac{a^{2}+2ab+64-x^{4}+4x^{3}-4x^{2}+4x^{3}-16x^{2}+16x-4x^{2}+16x-16}{\left(x-2\right)^{2}}$$

Combine like terms in a^{2}+2ab+64-x^{4}+4x^{3}-4x^{2}+4x^{3}-16x^{2}+16x-4x^{2}+16x-16.

$$\frac{a^{2}+2ab-24x^{2}+48-x^{4}+8x^{3}+32x}{\left(x-2\right)^{2}}$$

Expand \left(x-2\right)^{2}.

$$\frac{a^{2}+2ab-24x^{2}+48-x^{4}+8x^{3}+32x}{x^{2}-4x+4}$$