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

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

Evaluate

$$\frac{4a+7}{\left(a+2\right)^{2}}$$

Short Solution Steps

Factor a^{2}+4a+4.

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

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

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

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

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

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

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

Combine like terms in 3a+6+a+1.

$$\frac{4a+7}{\left(a+2\right)^{2}}$$

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

$$\frac{4a+7}{a^{2}+4a+4}$$

Expand

$$\frac{4a+7}{\left(a+2\right)^{2}}$$

Short Solution Steps

Factor a^{2}+4a+4.

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

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

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

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

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

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

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

Combine like terms in 3a+6+a+1.

$$\frac{4a+7}{\left(a+2\right)^{2}}$$

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

$$\frac{4a+7}{a^{2}+4a+4}$$