Solve x ^ 2 + 1/(x ^ 2) + 12(x + 1/x) + 38 | 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

$$x^{2}+\frac{1}{x^{2}}+12(x+\frac{1}{x})+38$$

Evaluate

$x^{2}+12x+38+\frac{12}{x}+\frac{1}{x^{2}}$

Short Solution Steps

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

$$x^{2}+\frac{1}{x^{2}}+12\left(\frac{xx}{x}+\frac{1}{x}\right)+38$$

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

$$x^{2}+\frac{1}{x^{2}}+12\times \frac{xx+1}{x}+38$$

Do the multiplications in $xx+1$.

$$x^{2}+\frac{1}{x^{2}}+12\times \frac{x^{2}+1}{x}+38$$

Express $12\times \frac{x^{2}+1}{x}$ as a single fraction.

$$x^{2}+\frac{1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}+38$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x^{2}+38$ times $\frac{x^{2}}{x^{2}}$.

$$\frac{\left(x^{2}+38\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

Since $\frac{\left(x^{2}+38\right)x^{2}}{x^{2}}$ and $\frac{1}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+38\right)x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

Do the multiplications in $\left(x^{2}+38\right)x^{2}+1$.

$$\frac{x^{4}+38x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

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

$$\frac{x^{4}+38x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)x}{x^{2}}$$

Since $\frac{x^{4}+38x^{2}+1}{x^{2}}$ and $\frac{12\left(x^{2}+1\right)x}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+38x^{2}+1+12\left(x^{2}+1\right)x}{x^{2}}$$

Do the multiplications in $x^{4}+38x^{2}+1+12\left(x^{2}+1\right)x$.

$$\frac{x^{4}+38x^{2}+1+12x^{3}+12x}{x^{2}}$$

Expand

$x^{2}+12x+38+\frac{12}{x}+\frac{1}{x^{2}}$

Short Solution Steps

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

$$x^{2}+\frac{1}{x^{2}}+12\left(\frac{xx}{x}+\frac{1}{x}\right)+38$$

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

$$x^{2}+\frac{1}{x^{2}}+12\times \frac{xx+1}{x}+38$$

Do the multiplications in $xx+1$.

$$x^{2}+\frac{1}{x^{2}}+12\times \frac{x^{2}+1}{x}+38$$

Express $12\times \frac{x^{2}+1}{x}$ as a single fraction.

$$x^{2}+\frac{1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}+38$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x^{2}+38$ times $\frac{x^{2}}{x^{2}}$.

$$\frac{\left(x^{2}+38\right)x^{2}}{x^{2}}+\frac{1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

Since $\frac{\left(x^{2}+38\right)x^{2}}{x^{2}}$ and $\frac{1}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+38\right)x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

Do the multiplications in $\left(x^{2}+38\right)x^{2}+1$.

$$\frac{x^{4}+38x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)}{x}$$

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

$$\frac{x^{4}+38x^{2}+1}{x^{2}}+\frac{12\left(x^{2}+1\right)x}{x^{2}}$$

Since $\frac{x^{4}+38x^{2}+1}{x^{2}}$ and $\frac{12\left(x^{2}+1\right)x}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{x^{4}+38x^{2}+1+12\left(x^{2}+1\right)x}{x^{2}}$$

Do the multiplications in $x^{4}+38x^{2}+1+12\left(x^{2}+1\right)x$.

$$\frac{x^{4}+38x^{2}+1+12x^{3}+12x}{x^{2}}$$