Solve ({left(3/x+1right)}^2+1

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

Evaluate

$$\frac{x^{2}+2x+10}{\left(x+1\right)^{2}}$$

Short Solution Steps

To raise \frac{3}{x+1} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x+1\right)^{2}}{\left(x+1\right)^{2}}.

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

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

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

Do the multiplications in 3^{2}+\left(x+1\right)^{2}.

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

Combine like terms in 3^{2}+x^{2}+2x+1.

$$\frac{10+x^{2}+2x}{\left(x+1\right)^{2}}$$

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

$$\frac{10+x^{2}+2x}{x^{2}+2x+1}$$

Expand

$$\frac{x^{2}+2x+10}{\left(x+1\right)^{2}}$$

Short Solution Steps

To raise \frac{3}{x+1} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x+1\right)^{2}}{\left(x+1\right)^{2}}.

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

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

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

Do the multiplications in 3^{2}+\left(x+1\right)^{2}.

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

Combine like terms in 3^{2}+x^{2}+2x+1.

$$\frac{10+x^{2}+2x}{\left(x+1\right)^{2}}$$

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

$$\frac{10+x^{2}+2x}{x^{2}+2x+1}$$