Solve f(2/a)=3(2/a)^2+3(a/a)-2

$$f ( \frac { 2 } { a } ) = 3 ( \frac { 2 } { a } ) ^ { 2 } + 3 ( \frac { a } { a } ) - 2$$

Evaluate

$$1+\frac{12}{a^{2}}$$

Short Solution Steps

Divide a by a to get 1.

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

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

$$3\times \frac{2^{2}}{a^{2}}+3\times 1-2$$

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

$$\frac{3\times 2^{2}}{a^{2}}+3\times 1-2$$

Multiply 3 and 1 to get 3.

$$\frac{3\times 2^{2}}{a^{2}}+3-2$$

Subtract 2 from 3 to get 1.

$$\frac{3\times 2^{2}}{a^{2}}+1$$

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

$$\frac{3\times 2^{2}}{a^{2}}+\frac{a^{2}}{a^{2}}$$

Since \frac{3\times 2^{2}}{a^{2}} and \frac{a^{2}}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2^{2}+a^{2}}{a^{2}}$$

Do the multiplications in 3\times 2^{2}+a^{2}.

$$\frac{12+a^{2}}{a^{2}}$$

Expand

$$1+\frac{12}{a^{2}}$$

Short Solution Steps

Divide a by a to get 1.

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

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

$$3\times \frac{2^{2}}{a^{2}}+3\times 1-2$$

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

$$\frac{3\times 2^{2}}{a^{2}}+3\times 1-2$$

Multiply 3 and 1 to get 3.

$$\frac{3\times 2^{2}}{a^{2}}+3-2$$

Subtract 2 from 3 to get 1.

$$\frac{3\times 2^{2}}{a^{2}}+1$$

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

$$\frac{3\times 2^{2}}{a^{2}}+\frac{a^{2}}{a^{2}}$$

Since \frac{3\times 2^{2}}{a^{2}} and \frac{a^{2}}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2^{2}+a^{2}}{a^{2}}$$

Do the multiplications in 3\times 2^{2}+a^{2}.

$$\frac{12+a^{2}}{a^{2}}$$