Solve iix * (x ^ 2 + 1/(x ^ 2)) ^ 2 - 4 * (x + 1/x) ^ 2 + 12 | 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

$$iix(x^{2}+\frac{1}{x^{2}})^{2}-4(x+\frac{1}{x})^{2}+12$$

Evaluate

$-x^{5}-4x^{2}-2x+4-\frac{4}{x^{2}}-\frac{1}{x^{3}}$

Solution Steps

Multiply $i$ and $i$ to get $-1$.

$$-x\left(x^{2}+\frac{1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

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

$$-x\left(\frac{x^{2}x^{2}}{x^{2}}+\frac{1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Since $\frac{x^{2}x^{2}}{x^{2}}$ and $\frac{1}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$-x\times \left(\frac{x^{2}x^{2}+1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Do the multiplications in $x^{2}x^{2}+1$.

$$-x\times \left(\frac{x^{4}+1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

To raise $\frac{x^{4}+1}{x^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$-x\times \frac{\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Express $x\times \frac{\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}$ as a single fraction.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(x+\frac{1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(\frac{xx}{x}+\frac{1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \left(\frac{xx+1}{x}\right)^{2}+12$$

Do the multiplications in $xx+1$.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \left(\frac{x^{2}+1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \frac{\left(x^{2}+1\right)^{2}}{x^{2}}+12$$

Express $4\times \frac{\left(x^{2}+1\right)^{2}}{x^{2}}$ as a single fraction.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-\frac{4\left(x^{2}+1\right)^{2}}{x^{2}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x^{2}\right)^{2}$ and $x^{2}$ is $x^{4}$. Multiply $\frac{4\left(x^{2}+1\right)^{2}}{x^{2}}$ times $\frac{x^{2}}{x^{2}}$.

$$-\frac{x\left(x^{4}+1\right)^{2}}{x^{4}}-\frac{4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}+12$$

Since $-\frac{x\left(x^{4}+1\right)^{2}}{x^{4}}$ and $\frac{4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x\left(x^{4}+1\right)^{2}-4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}+12$$

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

$$\frac{-x^{9}-2x^{5}-x-4x^{6}-8x^{4}-4x^{2}}{x^{4}}+12$$

Factor the expressions that are not already factored in $\frac{-x^{9}-2x^{5}-x-4x^{6}-8x^{4}-4x^{2}}{x^{4}}$.

$$\frac{x\left(-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1\right)}{x^{4}}+12$$

Cancel out $x$ in both numerator and denominator.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $12$ times $\frac{x^{3}}{x^{3}}$.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}+\frac{12x^{3}}{x^{3}}$$

Since $\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}$ and $\frac{12x^{3}}{x^{3}}$ have the same denominator, add them by adding their numerators.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1+12x^{3}}{x^{3}}$$

Combine like terms in $-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1+12x^{3}$.

$$\frac{-1-x^{8}-4x^{5}-2x^{4}+4x^{3}-4x}{x^{3}}$$

Expand

$-x^{5}-4x^{2}-2x+4-\frac{4}{x^{2}}-\frac{1}{x^{3}}$

Solution Steps

Multiply $i$ and $i$ to get $-1$.

$$-x\left(x^{2}+\frac{1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

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

$$-x\left(\frac{x^{2}x^{2}}{x^{2}}+\frac{1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Since $\frac{x^{2}x^{2}}{x^{2}}$ and $\frac{1}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$-x\times \left(\frac{x^{2}x^{2}+1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Do the multiplications in $x^{2}x^{2}+1$.

$$-x\times \left(\frac{x^{4}+1}{x^{2}}\right)^{2}-4\left(x+\frac{1}{x}\right)^{2}+12$$

To raise $\frac{x^{4}+1}{x^{2}}$ to a power, raise both numerator and denominator to the power and then divide.

$$-x\times \frac{\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(x+\frac{1}{x}\right)^{2}+12$$

Express $x\times \frac{\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}$ as a single fraction.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(x+\frac{1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\left(\frac{xx}{x}+\frac{1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \left(\frac{xx+1}{x}\right)^{2}+12$$

Do the multiplications in $xx+1$.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \left(\frac{x^{2}+1}{x}\right)^{2}+12$$

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

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-4\times \frac{\left(x^{2}+1\right)^{2}}{x^{2}}+12$$

Express $4\times \frac{\left(x^{2}+1\right)^{2}}{x^{2}}$ as a single fraction.

$$-\frac{x\left(x^{4}+1\right)^{2}}{\left(x^{2}\right)^{2}}-\frac{4\left(x^{2}+1\right)^{2}}{x^{2}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x^{2}\right)^{2}$ and $x^{2}$ is $x^{4}$. Multiply $\frac{4\left(x^{2}+1\right)^{2}}{x^{2}}$ times $\frac{x^{2}}{x^{2}}$.

$$-\frac{x\left(x^{4}+1\right)^{2}}{x^{4}}-\frac{4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}+12$$

Since $-\frac{x\left(x^{4}+1\right)^{2}}{x^{4}}$ and $\frac{4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x\left(x^{4}+1\right)^{2}-4\left(x^{2}+1\right)^{2}x^{2}}{x^{4}}+12$$

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

$$\frac{-x^{9}-2x^{5}-x-4x^{6}-8x^{4}-4x^{2}}{x^{4}}+12$$

Factor the expressions that are not already factored in $\frac{-x^{9}-2x^{5}-x-4x^{6}-8x^{4}-4x^{2}}{x^{4}}$.

$$\frac{x\left(-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1\right)}{x^{4}}+12$$

Cancel out $x$ in both numerator and denominator.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}+12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $12$ times $\frac{x^{3}}{x^{3}}$.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}+\frac{12x^{3}}{x^{3}}$$

Since $\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1}{x^{3}}$ and $\frac{12x^{3}}{x^{3}}$ have the same denominator, add them by adding their numerators.

$$\frac{-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1+12x^{3}}{x^{3}}$$

Combine like terms in $-x^{8}-4x^{5}-2x^{4}-8x^{3}-4x-1+12x^{3}$.

$$\frac{-1-x^{8}-4x^{5}-2x^{4}+4x^{3}-4x}{x^{3}}$$