Solve b/3+2/(frac{b{3})^2+1}

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

Evaluate

$$\frac{3\left(b+6\right)}{b^{2}+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

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

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

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

Do the multiplications in b+2\times 3.

$$\frac{\frac{b+6}{3}}{\left(\frac{b}{3}\right)^{2}+1}$$

To raise \frac{b}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}}{3^{2}}+1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3^{2}}{3^{2}}.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}}{3^{2}}+\frac{3^{2}}{3^{2}}}$$

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

$$\frac{\frac{b+6}{3}}{\frac{b^{2}+3^{2}}{3^{2}}}$$

Combine like terms in b^{2}+3^{2}.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}+9}{3^{2}}}$$

Divide \frac{b+6}{3} by \frac{b^{2}+9}{3^{2}} by multiplying \frac{b+6}{3} by the reciprocal of \frac{b^{2}+9}{3^{2}}.

$$\frac{\left(b+6\right)\times 3^{2}}{3\left(b^{2}+9\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(b+6\right)}{b^{2}+9}$$

Use the distributive property to multiply 3 by b+6.

$$\frac{3b+18}{b^{2}+9}$$

Expand

$$\frac{3\left(b+6\right)}{b^{2}+9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3}{3}.

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

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

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

Do the multiplications in b+2\times 3.

$$\frac{\frac{b+6}{3}}{\left(\frac{b}{3}\right)^{2}+1}$$

To raise \frac{b}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}}{3^{2}}+1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3^{2}}{3^{2}}.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}}{3^{2}}+\frac{3^{2}}{3^{2}}}$$

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

$$\frac{\frac{b+6}{3}}{\frac{b^{2}+3^{2}}{3^{2}}}$$

Combine like terms in b^{2}+3^{2}.

$$\frac{\frac{b+6}{3}}{\frac{b^{2}+9}{3^{2}}}$$

Divide \frac{b+6}{3} by \frac{b^{2}+9}{3^{2}} by multiplying \frac{b+6}{3} by the reciprocal of \frac{b^{2}+9}{3^{2}}.

$$\frac{\left(b+6\right)\times 3^{2}}{3\left(b^{2}+9\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(b+6\right)}{b^{2}+9}$$

Use the distributive property to multiply 3 by b+6.

$$\frac{3b+18}{b^{2}+9}$$