Solve (-1/2-3)(-1/2+1)-({left(-1/2right)}^2-2)

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

Evaluate

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Solution Steps

Convert 3 to fraction \frac{6}{2}.

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

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from -1 to get -7.

$$-\frac{7}{2}\left(-\frac{1}{2}+1\right)-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{7}{2}\left(-\frac{1}{2}+\frac{2}{2}\right)-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$-\frac{7}{2}\times \frac{-1+2}{2}-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Add -1 and 2 to get 1.

$$-\frac{7}{2}\times \frac{1}{2}-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Multiply -\frac{7}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7}{2\times 2}-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Do the multiplications in the fraction \frac{-7}{2\times 2}.

$$\frac{-7}{4}-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$-\frac{7}{4}-\left(\left(-\frac{1}{2}\right)^{2}-2\right)$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-\frac{7}{4}-\left(\frac{1}{4}-2\right)$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{7}{4}-\left(\frac{1}{4}-\frac{8}{4}\right)$$

Since \frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{4}-\frac{1-8}{4}$$

Subtract 8 from 1 to get -7.

$$-\frac{7}{4}-\left(-\frac{7}{4}\right)$$

The opposite of -\frac{7}{4} is \frac{7}{4}.

$$-\frac{7}{4}+\frac{7}{4}$$

Add -\frac{7}{4} and \frac{7}{4} to get 0.

$$0$$

Factor

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