Solve a+5/9a+4a-1/3a^2

$$\frac { a + 5 } { 9 a } + \frac { 4 a - 1 } { 3 a ^ { 2 } }$$

Evaluate

$$\frac{1}{9}+\frac{17}{9a}-\frac{1}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9a and 3a^{2} is 9a^{2}. Multiply \frac{a+5}{9a} times \frac{a}{a}. Multiply \frac{4a-1}{3a^{2}} times \frac{3}{3}.

$$\frac{\left(a+5\right)a}{9a^{2}}+\frac{3\left(4a-1\right)}{9a^{2}}$$

Since \frac{\left(a+5\right)a}{9a^{2}} and \frac{3\left(4a-1\right)}{9a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(a+5\right)a+3\left(4a-1\right)}{9a^{2}}$$

Do the multiplications in \left(a+5\right)a+3\left(4a-1\right).

$$\frac{a^{2}+5a+12a-3}{9a^{2}}$$

Combine like terms in a^{2}+5a+12a-3.

$$\frac{a^{2}+17a-3}{9a^{2}}$$

Expand

$$\frac{1}{9}+\frac{17}{9a}-\frac{1}{3a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9a and 3a^{2} is 9a^{2}. Multiply \frac{a+5}{9a} times \frac{a}{a}. Multiply \frac{4a-1}{3a^{2}} times \frac{3}{3}.

$$\frac{\left(a+5\right)a}{9a^{2}}+\frac{3\left(4a-1\right)}{9a^{2}}$$

Since \frac{\left(a+5\right)a}{9a^{2}} and \frac{3\left(4a-1\right)}{9a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(a+5\right)a+3\left(4a-1\right)}{9a^{2}}$$

Do the multiplications in \left(a+5\right)a+3\left(4a-1\right).

$$\frac{a^{2}+5a+12a-3}{9a^{2}}$$

Combine like terms in a^{2}+5a+12a-3.

$$\frac{a^{2}+17a-3}{9a^{2}}$$