Solve 1/81/{left(frac{2x+3{2}right)}^2+1}

$$\frac{ 1 }{ 8 } \frac{ 1 }{ { \left( \frac{ 2x+3 }{ 2 } \right) }^{ 2 } +1 }$$

Evaluate

$$\frac{1}{2\left(4x^{2}+12x+13\right)}$$

Short Solution Steps

To raise \frac{2x+3}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}}{2^{2}}+1}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}}{2^{2}}+\frac{2^{2}}{2^{2}}}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}+2^{2}}{2^{2}}}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{4x^{2}+12x+9+2^{2}}{2^{2}}}$$

Combine like terms in 4x^{2}+12x+9+2^{2}.

$$\frac{1}{8}\times \frac{1}{\frac{4x^{2}+12x+13}{2^{2}}}$$

Divide 1 by \frac{4x^{2}+12x+13}{2^{2}} by multiplying 1 by the reciprocal of \frac{4x^{2}+12x+13}{2^{2}}.

$$\frac{1}{8}\times \frac{2^{2}}{4x^{2}+12x+13}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{8}\times \frac{4}{4x^{2}+12x+13}$$

Multiply \frac{1}{8} times \frac{4}{4x^{2}+12x+13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{8\left(4x^{2}+12x+13\right)}$$

Use the distributive property to multiply 8 by 4x^{2}+12x+13.

$$\frac{4}{32x^{2}+96x+104}$$

Expand

$$\frac{1}{8\left(x^{2}+3x+\frac{13}{4}\right)}$$

Short Solution Steps

To raise \frac{2x+3}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}}{2^{2}}+1}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}}{2^{2}}+\frac{2^{2}}{2^{2}}}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{\left(2x+3\right)^{2}+2^{2}}{2^{2}}}$$

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

$$\frac{1}{8}\times \frac{1}{\frac{4x^{2}+12x+9+2^{2}}{2^{2}}}$$

Combine like terms in 4x^{2}+12x+9+2^{2}.

$$\frac{1}{8}\times \frac{1}{\frac{4x^{2}+12x+13}{2^{2}}}$$

Divide 1 by \frac{4x^{2}+12x+13}{2^{2}} by multiplying 1 by the reciprocal of \frac{4x^{2}+12x+13}{2^{2}}.

$$\frac{1}{8}\times \frac{2^{2}}{4x^{2}+12x+13}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{8}\times \frac{4}{4x^{2}+12x+13}$$

Multiply \frac{1}{8} times \frac{4}{4x^{2}+12x+13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{8\left(4x^{2}+12x+13\right)}$$

Use the distributive property to multiply 8 by 4x^{2}+12x+13.

$$\frac{4}{32x^{2}+96x+104}$$