Solve 1/x^2+2^23x+x/2x+17x

$$\frac{ 1 }{ { x }^{ 2 } } + { 2 }^{ 2 } 3x+ \frac{ x }{ 2x } +17x$$

Evaluate

$$29x+\frac{1}{2}+\frac{1}{x^{2}}$$

Short Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{x^{2}}+4\times 3x+\frac{x}{2x}+17x$$

Multiply 4 and 3 to get 12.

$$\frac{1}{x^{2}}+12x+\frac{x}{2x}+17x$$

Cancel out x in both numerator and denominator.

$$\frac{1}{x^{2}}+12x+\frac{1}{2}+17x$$

Combine 12x and 17x to get 29x.

$$\frac{1}{x^{2}}+29x+\frac{1}{2}$$

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

$$\frac{2}{2x^{2}}+29x+\frac{x^{2}}{2x^{2}}$$

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

$$\frac{2+x^{2}}{2x^{2}}+29x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 29x times \frac{2x^{2}}{2x^{2}}.

$$\frac{2+x^{2}}{2x^{2}}+\frac{29x\times 2x^{2}}{2x^{2}}$$

Since \frac{2+x^{2}}{2x^{2}} and \frac{29x\times 2x^{2}}{2x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{2+x^{2}+29x\times 2x^{2}}{2x^{2}}$$

Do the multiplications in 2+x^{2}+29x\times 2x^{2}.

$$\frac{2+x^{2}+58x^{3}}{2x^{2}}$$

Factor

$$\frac{58x^{3}+x^{2}+2}{2x^{2}}$$