Solve 4x^2+1/64x^2+1/2

$$4 x ^ { 2 } + \frac { 1 } { 64 x ^ { 2 } } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{\left(16x+\frac{1}{x}\right)^{2}}{64}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 64x^{2} and 2 is 64x^{2}. Multiply \frac{1}{2} times \frac{32x^{2}}{32x^{2}}.

$$4x^{2}+\frac{1}{64x^{2}}+\frac{32x^{2}}{64x^{2}}$$

Since \frac{1}{64x^{2}} and \frac{32x^{2}}{64x^{2}} have the same denominator, add them by adding their numerators.

$$4x^{2}+\frac{1+32x^{2}}{64x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2} times \frac{64x^{2}}{64x^{2}}.

$$\frac{4x^{2}\times 64x^{2}}{64x^{2}}+\frac{1+32x^{2}}{64x^{2}}$$

Since \frac{4x^{2}\times 64x^{2}}{64x^{2}} and \frac{1+32x^{2}}{64x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}\times 64x^{2}+1+32x^{2}}{64x^{2}}$$

Do the multiplications in 4x^{2}\times 64x^{2}+1+32x^{2}.

$$\frac{256x^{4}+1+32x^{2}}{64x^{2}}$$

Factor

$$\frac{\left(16x^{2}+1\right)^{2}}{64x^{2}}$$