Solve 1/2x^2+2x-1-(x^2+2x-(1/2x^2+x-1))

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

Evaluate

$$x-2$$

Solution Steps

To find the opposite of \frac{1}{2}x^{2}+x-1, find the opposite of each term.

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

Combine x^{2} and -\frac{1}{2}x^{2} to get \frac{1}{2}x^{2}.

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

Combine 2x and -x to get x.

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

To find the opposite of \frac{1}{2}x^{2}+x+1, find the opposite of each term.

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

Combine \frac{1}{2}x^{2} and -\frac{1}{2}x^{2} to get 0.

$$2x-1-x-1$$

Combine 2x and -x to get x.

$$x-1-1$$

Subtract 1 from -1 to get -2.

$$x-2$$

Expand

$$x-2$$

Solution Steps

To find the opposite of \frac{1}{2}x^{2}+x-1, find the opposite of each term.

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

Combine x^{2} and -\frac{1}{2}x^{2} to get \frac{1}{2}x^{2}.

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

Combine 2x and -x to get x.

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

To find the opposite of \frac{1}{2}x^{2}+x+1, find the opposite of each term.

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

Combine \frac{1}{2}x^{2} and -\frac{1}{2}x^{2} to get 0.

$$2x-1-x-1$$

Combine 2x and -x to get x.

$$x-1-1$$

Subtract 1 from -1 to get -2.

$$x-2$$