Solve 4x^2+3/8x^2+1/1024x^4

$$4 x ^ { 2 } + \frac { 3 } { 8 x ^ { 2 } } + \frac { 1 } { 1024 x ^ { 4 } }$$

Evaluate

$$4x^{2}+\frac{3}{8x^{2}}+\frac{1}{1024x^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2} times \frac{8x^{2}}{8x^{2}}.

$$\frac{4x^{2}\times 8x^{2}}{8x^{2}}+\frac{3}{8x^{2}}+\frac{1}{1024x^{4}}$$

Since \frac{4x^{2}\times 8x^{2}}{8x^{2}} and \frac{3}{8x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}\times 8x^{2}+3}{8x^{2}}+\frac{1}{1024x^{4}}$$

Do the multiplications in 4x^{2}\times 8x^{2}+3.

$$\frac{32x^{4}+3}{8x^{2}}+\frac{1}{1024x^{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8x^{2} and 1024x^{4} is 1024x^{4}. Multiply \frac{32x^{4}+3}{8x^{2}} times \frac{128x^{2}}{128x^{2}}.

$$\frac{\left(32x^{4}+3\right)\times 128x^{2}}{1024x^{4}}+\frac{1}{1024x^{4}}$$

Since \frac{\left(32x^{4}+3\right)\times 128x^{2}}{1024x^{4}} and \frac{1}{1024x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{\left(32x^{4}+3\right)\times 128x^{2}+1}{1024x^{4}}$$

Do the multiplications in \left(32x^{4}+3\right)\times 128x^{2}+1.

$$\frac{4096x^{6}+384x^{2}+1}{1024x^{4}}$$

Factor

$$\frac{4096x^{6}+384x^{2}+1}{1024x^{4}}$$