Solve f(x)=2x+3/2x-4-(3+3/2x-4)

$$f ( x ) = 2 x + \frac { 3 } { 2 x - 4 } - ( 3 + \frac { 3 } { 2 x - 4 } )$$

Evaluate

$$2x-3$$

Short Solution Steps

Factor 2x-4.

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

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

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

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

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

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)$$

Factor 2x-4.

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2\left(x-2\right)}\right)$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}\right)$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{3\times 2\left(x-2\right)+3}{2\left(x-2\right)}$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-12+3}{2\left(x-2\right)}$$

Combine like terms in 6x-12+3.

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-9}{2\left(x-2\right)}$$

Since \frac{4x^{2}-8x+3}{2\left(x-2\right)} and \frac{6x-9}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}-8x+3-\left(6x-9\right)}{2\left(x-2\right)}$$

Do the multiplications in 4x^{2}-8x+3-\left(6x-9\right).

$$\frac{4x^{2}-8x+3-6x+9}{2\left(x-2\right)}$$

Combine like terms in 4x^{2}-8x+3-6x+9.

$$\frac{4x^{2}-14x+12}{2\left(x-2\right)}$$

Factor the expressions that are not already factored in \frac{4x^{2}-14x+12}{2\left(x-2\right)}.

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

Cancel out 2\left(x-2\right) in both numerator and denominator.

$$2x-3$$

Expand

$$2x-3$$

Short Solution Steps

Factor 2x-4.

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

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

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

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

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

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2x-4}\right)$$

Factor 2x-4.

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(3+\frac{3}{2\left(x-2\right)}\right)$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\left(\frac{3\times 2\left(x-2\right)}{2\left(x-2\right)}+\frac{3}{2\left(x-2\right)}\right)$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{3\times 2\left(x-2\right)+3}{2\left(x-2\right)}$$

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

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-12+3}{2\left(x-2\right)}$$

Combine like terms in 6x-12+3.

$$\frac{4x^{2}-8x+3}{2\left(x-2\right)}-\frac{6x-9}{2\left(x-2\right)}$$

Since \frac{4x^{2}-8x+3}{2\left(x-2\right)} and \frac{6x-9}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4x^{2}-8x+3-\left(6x-9\right)}{2\left(x-2\right)}$$

Do the multiplications in 4x^{2}-8x+3-\left(6x-9\right).

$$\frac{4x^{2}-8x+3-6x+9}{2\left(x-2\right)}$$

Combine like terms in 4x^{2}-8x+3-6x+9.

$$\frac{4x^{2}-14x+12}{2\left(x-2\right)}$$

Factor the expressions that are not already factored in \frac{4x^{2}-14x+12}{2\left(x-2\right)}.

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

Cancel out 2\left(x-2\right) in both numerator and denominator.

$$2x-3$$