Solve (5x-(1)/(x))^(2)+4(5x-(1)/(x))+4 | 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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{x}{x}$.

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

Since $\frac{5xx}{x}$ and $\frac{1}{x}$ have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in $5xx-1$.

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

To raise $\frac{5x^{2}-1}{x}$ to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{x}{x}$.

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

Since $\frac{5xx}{x}$ and $\frac{1}{x}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x^{2}-1\right)^{2}}{x^{2}}+4\times \frac{5xx-1}{x}+4$$

Do the multiplications in $5xx-1$.

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

Express $4\times \frac{5x^{2}-1}{x}$ as a single fraction.

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

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 $\frac{4\left(5x^{2}-1\right)}{x}$ times $\frac{x}{x}$.

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

Since $\frac{\left(5x^{2}-1\right)^{2}}{x^{2}}$ and $\frac{4\left(5x^{2}-1\right)x}{x^{2}}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $\left(5x^{2}-1\right)^{2}+4\left(5x^{2}-1\right)x$.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $4$ times $\frac{x^{2}}{x^{2}}$.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}+\frac{4x^{2}}{x^{2}}$$

Since $\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}$ and $\frac{4x^{2}}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x+4x^{2}}{x^{2}}$$

Combine like terms in $25x^{4}-10x^{2}+1+20x^{3}-4x+4x^{2}$.

$$\frac{25x^{4}-6x^{2}+1+20x^{3}-4x}{x^{2}}$$

Expand

$25x^{2}+20x-6-\frac{4}{x}+\frac{1}{x^{2}}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{x}{x}$.

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

Since $\frac{5xx}{x}$ and $\frac{1}{x}$ have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in $5xx-1$.

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

To raise $\frac{5x^{2}-1}{x}$ to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{x}{x}$.

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

Since $\frac{5xx}{x}$ and $\frac{1}{x}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(5x^{2}-1\right)^{2}}{x^{2}}+4\times \frac{5xx-1}{x}+4$$

Do the multiplications in $5xx-1$.

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

Express $4\times \frac{5x^{2}-1}{x}$ as a single fraction.

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

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 $\frac{4\left(5x^{2}-1\right)}{x}$ times $\frac{x}{x}$.

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

Since $\frac{\left(5x^{2}-1\right)^{2}}{x^{2}}$ and $\frac{4\left(5x^{2}-1\right)x}{x^{2}}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $\left(5x^{2}-1\right)^{2}+4\left(5x^{2}-1\right)x$.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}+4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $4$ times $\frac{x^{2}}{x^{2}}$.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}+\frac{4x^{2}}{x^{2}}$$

Since $\frac{25x^{4}-10x^{2}+1+20x^{3}-4x}{x^{2}}$ and $\frac{4x^{2}}{x^{2}}$ have the same denominator, add them by adding their numerators.

$$\frac{25x^{4}-10x^{2}+1+20x^{3}-4x+4x^{2}}{x^{2}}$$

Combine like terms in $25x^{4}-10x^{2}+1+20x^{3}-4x+4x^{2}$.

$$\frac{25x^{4}-6x^{2}+1+20x^{3}-4x}{x^{2}}$$