Solve x(6x^2-4x+2)/2x-(6x-4x^2+8)/2

$$\frac { x ( 6 x ^ { 2 } - 4 x + 2 ) } { 2 x } - \frac { ( 6 x - 4 x ^ { 2 } + 8 ) } { 2 }$$

Evaluate

$$5x^{2}-5x-3$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{6x^{2}-4x+2}{2}-\frac{6x-4x^{2}+8}{2}$$

Divide each term of 6x^{2}-4x+2 by 2 to get 3x^{2}-2x+1.

$$3x^{2}-2x+1-\frac{6x-4x^{2}+8}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{2}-2x+1 times \frac{2}{2}.

$$\frac{2\left(3x^{2}-2x+1\right)}{2}-\frac{6x-4x^{2}+8}{2}$$

Since \frac{2\left(3x^{2}-2x+1\right)}{2} and \frac{6x-4x^{2}+8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(3x^{2}-2x+1\right)-\left(6x-4x^{2}+8\right)}{2}$$

Do the multiplications in 2\left(3x^{2}-2x+1\right)-\left(6x-4x^{2}+8\right).

$$\frac{6x^{2}-4x+2-6x+4x^{2}-8}{2}$$

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

$$\frac{10x^{2}-10x-6}{2}$$

Divide each term of 10x^{2}-10x-6 by 2 to get -3-5x+5x^{2}.

$$-3-5x+5x^{2}$$

Expand

$$5x^{2}-5x-3$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{6x^{2}-4x+2}{2}-\frac{6x-4x^{2}+8}{2}$$

Divide each term of 6x^{2}-4x+2 by 2 to get 3x^{2}-2x+1.

$$3x^{2}-2x+1-\frac{6x-4x^{2}+8}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{2}-2x+1 times \frac{2}{2}.

$$\frac{2\left(3x^{2}-2x+1\right)}{2}-\frac{6x-4x^{2}+8}{2}$$

Since \frac{2\left(3x^{2}-2x+1\right)}{2} and \frac{6x-4x^{2}+8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(3x^{2}-2x+1\right)-\left(6x-4x^{2}+8\right)}{2}$$

Do the multiplications in 2\left(3x^{2}-2x+1\right)-\left(6x-4x^{2}+8\right).

$$\frac{6x^{2}-4x+2-6x+4x^{2}-8}{2}$$

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

$$\frac{10x^{2}-10x-6}{2}$$

Divide each term of 10x^{2}-10x-6 by 2 to get -3-5x+5x^{2}.

$$-3-5x+5x^{2}$$