Solve (a+2/3+1/9a)*3a/3a+1=

$$( a + \frac { 2 } { 3 } + \frac { 1 } { 9 a } ) \cdot \frac { 3 a } { 3 a + 1 } =$$

Evaluate

$$a = \frac{1}{3} = 0.3333333333333333$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 9a is 9a. Multiply \frac{2}{3} times \frac{3a}{3a}.

$$\left(a+\frac{2\times 3a}{9a}+\frac{1}{9a}\right)\times \frac{3a}{3a+1}$$

Since \frac{2\times 3a}{9a} and \frac{1}{9a} have the same denominator, add them by adding their numerators.

$$\left(a+\frac{2\times 3a+1}{9a}\right)\times \frac{3a}{3a+1}$$

Do the multiplications in 2\times 3a+1.

$$\left(a+\frac{6a+1}{9a}\right)\times \frac{3a}{3a+1}$$

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

$$\left(\frac{a\times 9a}{9a}+\frac{6a+1}{9a}\right)\times \frac{3a}{3a+1}$$

Since \frac{a\times 9a}{9a} and \frac{6a+1}{9a} have the same denominator, add them by adding their numerators.

$$\frac{a\times 9a+6a+1}{9a}\times \frac{3a}{3a+1}$$

Do the multiplications in a\times 9a+6a+1.

$$\frac{9a^{2}+6a+1}{9a}\times \frac{3a}{3a+1}$$

Multiply \frac{9a^{2}+6a+1}{9a} times \frac{3a}{3a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9a^{2}+6a+1\right)\times 3a}{9a\left(3a+1\right)}$$

Cancel out 3a in both numerator and denominator.

$$\frac{9a^{2}+6a+1}{3\left(3a+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3a+1 in both numerator and denominator.

$$\frac{3a+1}{3}$$

Expand

$$a = \frac{1}{3} = 0.3333333333333333$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 9a is 9a. Multiply \frac{2}{3} times \frac{3a}{3a}.

$$\left(a+\frac{2\times 3a}{9a}+\frac{1}{9a}\right)\times \frac{3a}{3a+1}$$

Since \frac{2\times 3a}{9a} and \frac{1}{9a} have the same denominator, add them by adding their numerators.

$$\left(a+\frac{2\times 3a+1}{9a}\right)\times \frac{3a}{3a+1}$$

Do the multiplications in 2\times 3a+1.

$$\left(a+\frac{6a+1}{9a}\right)\times \frac{3a}{3a+1}$$

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

$$\left(\frac{a\times 9a}{9a}+\frac{6a+1}{9a}\right)\times \frac{3a}{3a+1}$$

Since \frac{a\times 9a}{9a} and \frac{6a+1}{9a} have the same denominator, add them by adding their numerators.

$$\frac{a\times 9a+6a+1}{9a}\times \frac{3a}{3a+1}$$

Do the multiplications in a\times 9a+6a+1.

$$\frac{9a^{2}+6a+1}{9a}\times \frac{3a}{3a+1}$$

Multiply \frac{9a^{2}+6a+1}{9a} times \frac{3a}{3a+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9a^{2}+6a+1\right)\times 3a}{9a\left(3a+1\right)}$$

Cancel out 3a in both numerator and denominator.

$$\frac{9a^{2}+6a+1}{3\left(3a+1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 3a+1 in both numerator and denominator.

$$\frac{3a+1}{3}$$