Solve (x-1/x)^2-6(x+1/x)+12=

$$( x - \frac { 1 } { x } ) ^ { 2 } - 6 ( x + \frac { 1 } { x } ) + 12 =$$

Evaluate

$$\left(\frac{x-1}{x}\right)^{2}\left(x^{2}-4x+1\right)$$

Short Solution Steps

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

$$\left(\frac{xx}{x}-\frac{1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{xx-1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

Do the multiplications in xx-1.

$$\left(\frac{x^{2}-1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

To raise \frac{x^{2}-1}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\left(x+\frac{1}{x}\right)+12$$

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

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\left(\frac{xx}{x}+\frac{1}{x}\right)+12$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\times \frac{xx+1}{x}+12$$

Do the multiplications in xx+1.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\times \frac{x^{2}+1}{x}+12$$

Express -6\times \frac{x^{2}+1}{x} as a single fraction.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}+\frac{-6\left(x^{2}+1\right)}{x}+12$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x is x^{2}. Multiply \frac{-6\left(x^{2}+1\right)}{x} times \frac{x}{x}.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}+\frac{-6\left(x^{2}+1\right)x}{x^{2}}+12$$

Since \frac{\left(x^{2}-1\right)^{2}}{x^{2}} and \frac{-6\left(x^{2}+1\right)x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-1\right)^{2}-6\left(x^{2}+1\right)x}{x^{2}}+12$$

Do the multiplications in \left(x^{2}-1\right)^{2}-6\left(x^{2}+1\right)x.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x^{2}}{x^{2}}.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}}+\frac{12x^{2}}{x^{2}}$$

Since \frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}} and \frac{12x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x+12x^{2}}{x^{2}}$$

Combine like terms in x^{4}-2x^{2}+1-6x^{3}-6x+12x^{2}.

$$\frac{x^{4}+10x^{2}+1-6x^{3}-6x}{x^{2}}$$

Expand

$$x^{2}-6x+10-\frac{6}{x}+\frac{1}{x^{2}}$$

Short Solution Steps

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

$$\left(\frac{xx}{x}-\frac{1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{xx-1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

Do the multiplications in xx-1.

$$\left(\frac{x^{2}-1}{x}\right)^{2}-6\left(x+\frac{1}{x}\right)+12$$

To raise \frac{x^{2}-1}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\left(x+\frac{1}{x}\right)+12$$

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

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\left(\frac{xx}{x}+\frac{1}{x}\right)+12$$

Since \frac{xx}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\times \frac{xx+1}{x}+12$$

Do the multiplications in xx+1.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}-6\times \frac{x^{2}+1}{x}+12$$

Express -6\times \frac{x^{2}+1}{x} as a single fraction.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}+\frac{-6\left(x^{2}+1\right)}{x}+12$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and x is x^{2}. Multiply \frac{-6\left(x^{2}+1\right)}{x} times \frac{x}{x}.

$$\frac{\left(x^{2}-1\right)^{2}}{x^{2}}+\frac{-6\left(x^{2}+1\right)x}{x^{2}}+12$$

Since \frac{\left(x^{2}-1\right)^{2}}{x^{2}} and \frac{-6\left(x^{2}+1\right)x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-1\right)^{2}-6\left(x^{2}+1\right)x}{x^{2}}+12$$

Do the multiplications in \left(x^{2}-1\right)^{2}-6\left(x^{2}+1\right)x.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x^{2}}{x^{2}}.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}}+\frac{12x^{2}}{x^{2}}$$

Since \frac{x^{4}-2x^{2}+1-6x^{3}-6x}{x^{2}} and \frac{12x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}-2x^{2}+1-6x^{3}-6x+12x^{2}}{x^{2}}$$

Combine like terms in x^{4}-2x^{2}+1-6x^{3}-6x+12x^{2}.

$$\frac{x^{4}+10x^{2}+1-6x^{3}-6x}{x^{2}}$$