Solve x^2+1/x^2-7(x-1/x)+8

$$x ^ { 2 } + \frac { 1 } { x ^ { 2 } } - 7 ( x - \frac { 1 } { x } ) + 8$$

Evaluate

$$x^{2}-7x+8+\frac{7}{x}+\frac{1}{x^{2}}$$

Short Solution Steps

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

$$x^{2}+\frac{1}{x^{2}}-7\left(\frac{xx}{x}-\frac{1}{x}\right)+8$$

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

$$x^{2}+\frac{1}{x^{2}}-7\times \frac{xx-1}{x}+8$$

Do the multiplications in xx-1.

$$x^{2}+\frac{1}{x^{2}}-7\times \frac{x^{2}-1}{x}+8$$

Express -7\times \frac{x^{2}-1}{x} as a single fraction.

$$x^{2}+\frac{1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}+8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+8 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{2}+8\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

Since \frac{\left(x^{2}+8\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+8\right)x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

Do the multiplications in \left(x^{2}+8\right)x^{2}+1.

$$\frac{x^{4}+8x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

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{-7\left(x^{2}-1\right)}{x} times \frac{x}{x}.

$$\frac{x^{4}+8x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)x}{x^{2}}$$

Since \frac{x^{4}+8x^{2}+1}{x^{2}} and \frac{-7\left(x^{2}-1\right)x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+8x^{2}+1-7\left(x^{2}-1\right)x}{x^{2}}$$

Do the multiplications in x^{4}+8x^{2}+1-7\left(x^{2}-1\right)x.

$$\frac{x^{4}+8x^{2}+1-7x^{3}+7x}{x^{2}}$$

Expand

$$x^{2}-7x+8+\frac{7}{x}+\frac{1}{x^{2}}$$

Short Solution Steps

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

$$x^{2}+\frac{1}{x^{2}}-7\left(\frac{xx}{x}-\frac{1}{x}\right)+8$$

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

$$x^{2}+\frac{1}{x^{2}}-7\times \frac{xx-1}{x}+8$$

Do the multiplications in xx-1.

$$x^{2}+\frac{1}{x^{2}}-7\times \frac{x^{2}-1}{x}+8$$

Express -7\times \frac{x^{2}-1}{x} as a single fraction.

$$x^{2}+\frac{1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}+8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+8 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(x^{2}+8\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

Since \frac{\left(x^{2}+8\right)x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+8\right)x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

Do the multiplications in \left(x^{2}+8\right)x^{2}+1.

$$\frac{x^{4}+8x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)}{x}$$

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{-7\left(x^{2}-1\right)}{x} times \frac{x}{x}.

$$\frac{x^{4}+8x^{2}+1}{x^{2}}+\frac{-7\left(x^{2}-1\right)x}{x^{2}}$$

Since \frac{x^{4}+8x^{2}+1}{x^{2}} and \frac{-7\left(x^{2}-1\right)x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+8x^{2}+1-7\left(x^{2}-1\right)x}{x^{2}}$$

Do the multiplications in x^{4}+8x^{2}+1-7\left(x^{2}-1\right)x.

$$\frac{x^{4}+8x^{2}+1-7x^{3}+7x}{x^{2}}$$