Solve a/(3a+1)^2+4/3a+1

$$\frac { a } { ( 3 a + 1 ) ^ { 2 } } + \frac { 4 } { 3 a + 1 }$$

Evaluate

$$\frac{13a+4}{\left(3a+1\right)^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{a+12a+4}{\left(3a+1\right)^{2}}$$

Combine like terms in a+12a+4.

$$\frac{13a+4}{\left(3a+1\right)^{2}}$$

Expand \left(3a+1\right)^{2}.

$$\frac{13a+4}{9a^{2}+6a+1}$$

Expand

$$\frac{13a+4}{\left(3a+1\right)^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{a+12a+4}{\left(3a+1\right)^{2}}$$

Combine like terms in a+12a+4.

$$\frac{13a+4}{\left(3a+1\right)^{2}}$$

Expand \left(3a+1\right)^{2}.

$$\frac{13a+4}{9a^{2}+6a+1}$$