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

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

Evaluate

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

Short Solution Steps

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

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

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

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

To raise \frac{3+2x}{x} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Since \frac{\left(3+2x\right)^{2}}{x^{2}} and \frac{\left(2x-3\right)^{2}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{9+12x+4x^{2}-4x^{4}+12x^{3}-9x^{2}}{x^{2}}$$

Combine like terms in 9+12x+4x^{2}-4x^{4}+12x^{3}-9x^{2}.

$$\frac{9+12x-5x^{2}-4x^{4}+12x^{3}}{x^{2}}$$

Expand

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

Short Solution Steps

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

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

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

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

To raise \frac{3+2x}{x} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Since \frac{\left(3+2x\right)^{2}}{x^{2}} and \frac{\left(2x-3\right)^{2}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{9+12x+4x^{2}-4x^{4}+12x^{3}-9x^{2}}{x^{2}}$$

Combine like terms in 9+12x+4x^{2}-4x^{4}+12x^{3}-9x^{2}.

$$\frac{9+12x-5x^{2}-4x^{4}+12x^{3}}{x^{2}}$$