Solve (x+(2)/(x)-3)(x-(2)/(3)-3) | 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

$$(x+ \frac{ 2 }{ x } -3)(x- \frac{ 2 }{ 3 } -3)$$

Evaluate

$x^{2}-\frac{20x}{3}+13-\frac{22}{3x}$

Short Solution Steps

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

$$\left(\frac{\left(x-3\right)x}{x}+\frac{2}{x}\right)\left(x-\frac{2}{3}-3\right)$$

Since $\frac{\left(x-3\right)x}{x}$ and $\frac{2}{x}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x-3\right)x+2}{x}\left(x-\frac{2}{3}-3\right)$$

Do the multiplications in $\left(x-3\right)x+2$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{2}{3}-3\right)$$

Convert $3$ to fraction $\frac{9}{3}$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{2}{3}-\frac{9}{3}\right)$$

Since $-\frac{2}{3}$ and $\frac{9}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-3x+2}{x}\left(x+\frac{-2-9}{3}\right)$$

Subtract $9$ from $-2$ to get $-11$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{11}{3}\right)$$

Use the distributive property to multiply $\frac{x^{2}-3x+2}{x}$ by $x-\frac{11}{3}$.

$$\frac{x^{2}-3x+2}{x}x+\frac{x^{2}-3x+2}{x}\left(-\frac{11}{3}\right)$$

Cancel out $x$ and $x$.

$$x^{2}-3x+2+\frac{x^{2}-3x+2}{x}\left(-\frac{11}{3}\right)$$

Multiply $\frac{x^{2}-3x+2}{x}$ times $-\frac{11}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-3x+2+\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x^{2}-3x+2$ times $\frac{x\times 3}{x\times 3}$.

$$\frac{\left(x^{2}-3x+2\right)x\times 3}{x\times 3}+\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

Since $\frac{\left(x^{2}-3x+2\right)x\times 3}{x\times 3}$ and $\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-3x+2\right)x\times 3-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

Do the multiplications in $\left(x^{2}-3x+2\right)x\times 3-\left(x^{2}-3x+2\right)\times 11$.

$$\frac{3x^{3}-9x^{2}+6x-11x^{2}+33x-22}{x\times 3}$$

Combine like terms in $3x^{3}-9x^{2}+6x-11x^{2}+33x-22$.

$$\frac{3x^{3}-20x^{2}+39x-22}{x\times 3}$$

Expand

$x^{2}-\frac{20x}{3}+13-\frac{22}{3x}$

Short Solution Steps

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

$$\left(\frac{\left(x-3\right)x}{x}+\frac{2}{x}\right)\left(x-\frac{2}{3}-3\right)$$

Since $\frac{\left(x-3\right)x}{x}$ and $\frac{2}{x}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x-3\right)x+2}{x}\left(x-\frac{2}{3}-3\right)$$

Do the multiplications in $\left(x-3\right)x+2$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{2}{3}-3\right)$$

Convert $3$ to fraction $\frac{9}{3}$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{2}{3}-\frac{9}{3}\right)$$

Since $-\frac{2}{3}$ and $\frac{9}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-3x+2}{x}\left(x+\frac{-2-9}{3}\right)$$

Subtract $9$ from $-2$ to get $-11$.

$$\frac{x^{2}-3x+2}{x}\left(x-\frac{11}{3}\right)$$

Use the distributive property to multiply $\frac{x^{2}-3x+2}{x}$ by $x-\frac{11}{3}$.

$$\frac{x^{2}-3x+2}{x}x+\frac{x^{2}-3x+2}{x}\left(-\frac{11}{3}\right)$$

Cancel out $x$ and $x$.

$$x^{2}-3x+2+\frac{x^{2}-3x+2}{x}\left(-\frac{11}{3}\right)$$

Multiply $\frac{x^{2}-3x+2}{x}$ times $-\frac{11}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$x^{2}-3x+2+\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x^{2}-3x+2$ times $\frac{x\times 3}{x\times 3}$.

$$\frac{\left(x^{2}-3x+2\right)x\times 3}{x\times 3}+\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

Since $\frac{\left(x^{2}-3x+2\right)x\times 3}{x\times 3}$ and $\frac{-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$ have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-3x+2\right)x\times 3-\left(x^{2}-3x+2\right)\times 11}{x\times 3}$$

Do the multiplications in $\left(x^{2}-3x+2\right)x\times 3-\left(x^{2}-3x+2\right)\times 11$.

$$\frac{3x^{3}-9x^{2}+6x-11x^{2}+33x-22}{x\times 3}$$

Combine like terms in $3x^{3}-9x^{2}+6x-11x^{2}+33x-22$.

$$\frac{3x^{3}-20x^{2}+39x-22}{x\times 3}$$