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

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

Evaluate

$$-9+\frac{4}{x^{2}}$$

Short Solution Steps

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

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

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

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

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

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

Since \frac{2}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

$$\frac{2-3x}{x}\times \frac{2+3x}{x}$$

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

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

Multiply x and x to get x^{2}.

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

Consider \left(2-3x\right)\left(2+3x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4-\left(3x\right)^{2}}{x^{2}}$$

Expand \left(3x\right)^{2}.

$$\frac{4-3^{2}x^{2}}{x^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4-9x^{2}}{x^{2}}$$

Expand

$$-9+\frac{4}{x^{2}}$$

Short Solution Steps

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

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

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

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

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

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

Since \frac{2}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

$$\frac{2-3x}{x}\times \frac{2+3x}{x}$$

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

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

Multiply x and x to get x^{2}.

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

Consider \left(2-3x\right)\left(2+3x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4-\left(3x\right)^{2}}{x^{2}}$$

Expand \left(3x\right)^{2}.

$$\frac{4-3^{2}x^{2}}{x^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4-9x^{2}}{x^{2}}$$