Solve 3/a+(1/2*b/a)^2

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

Evaluate

$$\frac{12a+b^{2}}{4a^{2}}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{a}+\left(\frac{b}{2a}\right)^{2}$$

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

$$\frac{3}{a}+\frac{b^{2}}{\left(2a\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and \left(2a\right)^{2} is a\times \left(2a\right)^{2}. Multiply \frac{3}{a} times \frac{\left(2a\right)^{2}}{\left(2a\right)^{2}}. Multiply \frac{b^{2}}{\left(2a\right)^{2}} times \frac{a}{a}.

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

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

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

Expand \left(2a\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{a}+\frac{b^{2}}{4a^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 4a^{2} is 4a^{2}. Multiply \frac{3}{a} times \frac{4a}{4a}.

$$\frac{3\times 4a}{4a^{2}}+\frac{b^{2}}{4a^{2}}$$

Since \frac{3\times 4a}{4a^{2}} and \frac{b^{2}}{4a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\times 4a+b^{2}}{4a^{2}}$$

Do the multiplications in 3\times 4a+b^{2}.

$$\frac{12a+b^{2}}{4a^{2}}$$

Expand

$$\frac{12a+b^{2}}{4a^{2}}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{b}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{a}+\left(\frac{b}{2a}\right)^{2}$$

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

$$\frac{3}{a}+\frac{b^{2}}{\left(2a\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and \left(2a\right)^{2} is a\times \left(2a\right)^{2}. Multiply \frac{3}{a} times \frac{\left(2a\right)^{2}}{\left(2a\right)^{2}}. Multiply \frac{b^{2}}{\left(2a\right)^{2}} times \frac{a}{a}.

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

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

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

Expand \left(2a\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{a}+\frac{b^{2}}{4a^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 4a^{2} is 4a^{2}. Multiply \frac{3}{a} times \frac{4a}{4a}.

$$\frac{3\times 4a}{4a^{2}}+\frac{b^{2}}{4a^{2}}$$

Since \frac{3\times 4a}{4a^{2}} and \frac{b^{2}}{4a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\times 4a+b^{2}}{4a^{2}}$$

Do the multiplications in 3\times 4a+b^{2}.

$$\frac{12a+b^{2}}{4a^{2}}$$