What is 1/2 (x^2+1)-3/2 (x^2-1) ?

The solution to 1/2 (x^2+1)-3/2 (x^2-1) is -x^2+2

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simplify 1/2 (x^2+1)-3/2 (x^2-1)

simplify

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

- x^{2} + 2

Solution steps

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

Expand

\frac{1}{2} (x^{2} + 1) : \frac{x ^{2}}{2} + \frac{1}{2}

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

Expand

- \frac{3}{2} (x^{2} - 1) : - \frac{3 x ^{2}}{2} + \frac{3}{2}

= \frac{x ^{2}}{2} + \frac{1}{2} - \frac{3 x ^{2}}{2} + \frac{3}{2}

Join

\frac{x ^{2}}{2} + \frac{1}{2} - \frac{3 x ^{2}}{2} + \frac{3}{2} : - x^{2} + 2

= - x^{2} + 2

2 x^{2} + 6 x + 8 x^{3} - 12 x^{4}

5 14 z^{2} \cdot 4 21 z^{3}

- 5 (x + 2) + 5 (x - 5)

\frac{x ^{2} - 16}{x ^{2} + 9 x + 20} \cdot \frac{x + 5}{x ^{2} - 7 x + 12}

(4^{5})^{3}

What is 1/2 (x^2+1)-3/2 (x^2-1) ?
The solution to 1/2 (x^2+1)-3/2 (x^2-1) is -x^2+2