Solve (2x-1/2)(3+1/x)=

$$( 2 x - \frac { 1 } { 2 } ) ( 3 + \frac { 1 } { x } ) =$$

Evaluate

$$6x+\frac{1}{2}-\frac{1}{2x}$$

Short Solution Steps

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

$$\left(2x-\frac{1}{2}\right)\left(\frac{3x}{x}+\frac{1}{x}\right)$$

Since \frac{3x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\left(2x-\frac{1}{2}\right)\times \frac{3x+1}{x}$$

Use the distributive property to multiply 2x-\frac{1}{2} by \frac{3x+1}{x}.

$$2x\times \frac{3x+1}{x}-\frac{1}{2}\times \frac{3x+1}{x}$$

Express 2\times \frac{3x+1}{x} as a single fraction.

$$\frac{2\left(3x+1\right)}{x}x-\frac{1}{2}\times \frac{3x+1}{x}$$

Multiply -\frac{1}{2} times \frac{3x+1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(3x+1\right)}{x}x+\frac{-\left(3x+1\right)}{2x}$$

Use the distributive property to multiply 2 by 3x+1.

$$\frac{6x+2}{x}x+\frac{-\left(3x+1\right)}{2x}$$

Cancel out x and x.

$$6x+2+\frac{-\left(3x+1\right)}{2x}$$

Cancel out -1 in both numerator and denominator.

$$6x+2+\frac{3x+1}{-2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x+2 times \frac{-2x}{-2x}.

$$\frac{\left(6x+2\right)\left(-2\right)x}{-2x}+\frac{3x+1}{-2x}$$

Since \frac{\left(6x+2\right)\left(-2\right)x}{-2x} and \frac{3x+1}{-2x} have the same denominator, add them by adding their numerators.

$$\frac{\left(6x+2\right)\left(-2\right)x+3x+1}{-2x}$$

Do the multiplications in \left(6x+2\right)\left(-2\right)x+3x+1.

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

Combine like terms in -12x^{2}-4x+3x+1.

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

Expand

$$6x+\frac{1}{2}-\frac{1}{2x}$$

Short Solution Steps

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

$$\left(2x-\frac{1}{2}\right)\left(\frac{3x}{x}+\frac{1}{x}\right)$$

Since \frac{3x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\left(2x-\frac{1}{2}\right)\times \frac{3x+1}{x}$$

Use the distributive property to multiply 2x-\frac{1}{2} by \frac{3x+1}{x}.

$$2x\times \frac{3x+1}{x}-\frac{1}{2}\times \frac{3x+1}{x}$$

Express 2\times \frac{3x+1}{x} as a single fraction.

$$\frac{2\left(3x+1\right)}{x}x-\frac{1}{2}\times \frac{3x+1}{x}$$

Multiply -\frac{1}{2} times \frac{3x+1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(3x+1\right)}{x}x+\frac{-\left(3x+1\right)}{2x}$$

Use the distributive property to multiply 2 by 3x+1.

$$\frac{6x+2}{x}x+\frac{-\left(3x+1\right)}{2x}$$

Cancel out x and x.

$$6x+2+\frac{-\left(3x+1\right)}{2x}$$

Cancel out -1 in both numerator and denominator.

$$6x+2+\frac{3x+1}{-2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x+2 times \frac{-2x}{-2x}.

$$\frac{\left(6x+2\right)\left(-2\right)x}{-2x}+\frac{3x+1}{-2x}$$

Since \frac{\left(6x+2\right)\left(-2\right)x}{-2x} and \frac{3x+1}{-2x} have the same denominator, add them by adding their numerators.

$$\frac{\left(6x+2\right)\left(-2\right)x+3x+1}{-2x}$$

Do the multiplications in \left(6x+2\right)\left(-2\right)x+3x+1.

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

Combine like terms in -12x^{2}-4x+3x+1.

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