Solve (x + 1/x) ^ 2 + (x - 1/x) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in $xx+1$.

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

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

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

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

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

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

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

Do the multiplications in $xx-1$.

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

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

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

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

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

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

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

Combine like terms in $x^{4}+2x^{2}+1+x^{4}-2x^{2}+1$.

$$\frac{2x^{4}+2}{x^{2}}$$

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in $xx+1$.

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

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

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

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

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

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

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

Do the multiplications in $xx-1$.

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

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

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

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

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

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

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

Combine like terms in $x^{4}+2x^{2}+1+x^{4}-2x^{2}+1$.

$$\frac{2x^{4}+2}{x^{2}}$$