Solve 2a-1/3a^2+5a+1/9a

$$\frac { 2 a - 1 } { 3 a ^ { 2 } } + \frac { 5 a + 1 } { 9 a }$$

Evaluate

$$\frac{5}{9}+\frac{7}{9a}-\frac{1}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a^{2} and 9a is 9a^{2}. Multiply \frac{2a-1}{3a^{2}} times \frac{3}{3}. Multiply \frac{5a+1}{9a} times \frac{a}{a}.

$$\frac{3\left(2a-1\right)}{9a^{2}}+\frac{\left(5a+1\right)a}{9a^{2}}$$

Since \frac{3\left(2a-1\right)}{9a^{2}} and \frac{\left(5a+1\right)a}{9a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\left(2a-1\right)+\left(5a+1\right)a}{9a^{2}}$$

Do the multiplications in 3\left(2a-1\right)+\left(5a+1\right)a.

$$\frac{6a-3+5a^{2}+a}{9a^{2}}$$

Combine like terms in 6a-3+5a^{2}+a.

$$\frac{7a-3+5a^{2}}{9a^{2}}$$

Expand

$$\frac{5}{9}+\frac{7}{9a}-\frac{1}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3a^{2} and 9a is 9a^{2}. Multiply \frac{2a-1}{3a^{2}} times \frac{3}{3}. Multiply \frac{5a+1}{9a} times \frac{a}{a}.

$$\frac{3\left(2a-1\right)}{9a^{2}}+\frac{\left(5a+1\right)a}{9a^{2}}$$

Since \frac{3\left(2a-1\right)}{9a^{2}} and \frac{\left(5a+1\right)a}{9a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\left(2a-1\right)+\left(5a+1\right)a}{9a^{2}}$$

Do the multiplications in 3\left(2a-1\right)+\left(5a+1\right)a.

$$\frac{6a-3+5a^{2}+a}{9a^{2}}$$

Combine like terms in 6a-3+5a^{2}+a.

$$\frac{7a-3+5a^{2}}{9a^{2}}$$