Solve 2-2(a/2)^2/1+(frac{a{2})^2}

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

Evaluate

$$-\frac{2\left(a^{2}-4\right)}{a^{2}+4}$$

Short Solution Steps

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{a^{2}}{2^{2}} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

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

Since \frac{2\times 2}{2} and \frac{a^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 2-a^{2}.

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

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{4-a^{2}}{2}}{1+\frac{a^{2}}{2^{2}}}$$

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

$$\frac{\frac{4-a^{2}}{2}}{\frac{2^{2}}{2^{2}}+\frac{a^{2}}{2^{2}}}$$

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

$$\frac{\frac{4-a^{2}}{2}}{\frac{2^{2}+a^{2}}{2^{2}}}$$

Combine like terms in 2^{2}+a^{2}.

$$\frac{\frac{4-a^{2}}{2}}{\frac{4+a^{2}}{2^{2}}}$$

Divide \frac{4-a^{2}}{2} by \frac{4+a^{2}}{2^{2}} by multiplying \frac{4-a^{2}}{2} by the reciprocal of \frac{4+a^{2}}{2^{2}}.

$$\frac{\left(4-a^{2}\right)\times 2^{2}}{2\left(4+a^{2}\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(-a^{2}+4\right)}{a^{2}+4}$$

Use the distributive property to multiply 2 by -a^{2}+4.

$$\frac{-2a^{2}+8}{a^{2}+4}$$

Expand

$$-\frac{2\left(a^{2}-4\right)}{a^{2}+4}$$

Short Solution Steps

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{a^{2}}{2^{2}} as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

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

Since \frac{2\times 2}{2} and \frac{a^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 2-a^{2}.

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

To raise \frac{a}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{4-a^{2}}{2}}{1+\frac{a^{2}}{2^{2}}}$$

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

$$\frac{\frac{4-a^{2}}{2}}{\frac{2^{2}}{2^{2}}+\frac{a^{2}}{2^{2}}}$$

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

$$\frac{\frac{4-a^{2}}{2}}{\frac{2^{2}+a^{2}}{2^{2}}}$$

Combine like terms in 2^{2}+a^{2}.

$$\frac{\frac{4-a^{2}}{2}}{\frac{4+a^{2}}{2^{2}}}$$

Divide \frac{4-a^{2}}{2} by \frac{4+a^{2}}{2^{2}} by multiplying \frac{4-a^{2}}{2} by the reciprocal of \frac{4+a^{2}}{2^{2}}.

$$\frac{\left(4-a^{2}\right)\times 2^{2}}{2\left(4+a^{2}\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(-a^{2}+4\right)}{a^{2}+4}$$

Use the distributive property to multiply 2 by -a^{2}+4.

$$\frac{-2a^{2}+8}{a^{2}+4}$$