Solve b/3+9/(b/3)^2+6

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

Evaluate

$$\frac{3\left(b+27\right)}{b^{2}+54}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{3}{3}.

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

Since \frac{b}{3} and \frac{9\times 3}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in b+9\times 3.

$$\frac{\frac{b+27}{3}}{\left(\frac{b}{3}\right)^{2}+6}$$

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

$$\frac{\frac{b+27}{3}}{\frac{b^{2}}{3^{2}}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{3^{2}}{3^{2}}.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}}{3^{2}}+\frac{6\times 3^{2}}{3^{2}}}$$

Since \frac{b^{2}}{3^{2}} and \frac{6\times 3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}+6\times 3^{2}}{3^{2}}}$$

Do the multiplications in b^{2}+6\times 3^{2}.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}+54}{3^{2}}}$$

Divide \frac{b+27}{3} by \frac{b^{2}+54}{3^{2}} by multiplying \frac{b+27}{3} by the reciprocal of \frac{b^{2}+54}{3^{2}}.

$$\frac{\left(b+27\right)\times 3^{2}}{3\left(b^{2}+54\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(b+27\right)}{b^{2}+54}$$

Use the distributive property to multiply 3 by b+27.

$$\frac{3b+81}{b^{2}+54}$$

Expand

$$\frac{3\left(b+27\right)}{b^{2}+54}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{3}{3}.

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

Since \frac{b}{3} and \frac{9\times 3}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in b+9\times 3.

$$\frac{\frac{b+27}{3}}{\left(\frac{b}{3}\right)^{2}+6}$$

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

$$\frac{\frac{b+27}{3}}{\frac{b^{2}}{3^{2}}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{3^{2}}{3^{2}}.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}}{3^{2}}+\frac{6\times 3^{2}}{3^{2}}}$$

Since \frac{b^{2}}{3^{2}} and \frac{6\times 3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}+6\times 3^{2}}{3^{2}}}$$

Do the multiplications in b^{2}+6\times 3^{2}.

$$\frac{\frac{b+27}{3}}{\frac{b^{2}+54}{3^{2}}}$$

Divide \frac{b+27}{3} by \frac{b^{2}+54}{3^{2}} by multiplying \frac{b+27}{3} by the reciprocal of \frac{b^{2}+54}{3^{2}}.

$$\frac{\left(b+27\right)\times 3^{2}}{3\left(b^{2}+54\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{3\left(b+27\right)}{b^{2}+54}$$

Use the distributive property to multiply 3 by b+27.

$$\frac{3b+81}{b^{2}+54}$$