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

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

Evaluate

$$-\frac{1}{3}+\frac{12}{y^{2}}$$

Short Solution Steps

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

$$3\times \frac{2^{2}}{y^{2}}-\frac{1}{3}$$

Express 3\times \frac{2^{2}}{y^{2}} as a single fraction.

$$\frac{3\times 2^{2}}{y^{2}}-\frac{1}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and 3 is 3y^{2}. Multiply \frac{3\times 2^{2}}{y^{2}} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{y^{2}}{y^{2}}.

$$\frac{3\times 3\times 2^{2}}{3y^{2}}-\frac{y^{2}}{3y^{2}}$$

Since \frac{3\times 3\times 2^{2}}{3y^{2}} and \frac{y^{2}}{3y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3\times 2^{2}-y^{2}}{3y^{2}}$$

Do the multiplications in 3\times 3\times 2^{2}-y^{2}.

$$\frac{36-y^{2}}{3y^{2}}$$

Expand

$$-\frac{1}{3}+\frac{12}{y^{2}}$$

Short Solution Steps

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

$$3\times \frac{2^{2}}{y^{2}}-\frac{1}{3}$$

Express 3\times \frac{2^{2}}{y^{2}} as a single fraction.

$$\frac{3\times 2^{2}}{y^{2}}-\frac{1}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and 3 is 3y^{2}. Multiply \frac{3\times 2^{2}}{y^{2}} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{y^{2}}{y^{2}}.

$$\frac{3\times 3\times 2^{2}}{3y^{2}}-\frac{y^{2}}{3y^{2}}$$

Since \frac{3\times 3\times 2^{2}}{3y^{2}} and \frac{y^{2}}{3y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3\times 2^{2}-y^{2}}{3y^{2}}$$

Do the multiplications in 3\times 3\times 2^{2}-y^{2}.

$$\frac{36-y^{2}}{3y^{2}}$$