Solve 1/22x/x^2+5+1/x

$$\frac{ 1 }{ 2 } \frac{ 2x }{ { x }^{ 2 } +5 } + \frac{ 1 }{ x }$$

Evaluate

$$\frac{2x^{2}+5}{x\left(x^{2}+5\right)}$$

Short Solution Steps

Multiply \frac{1}{2} times \frac{2x}{x^{2}+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x}{2\left(x^{2}+5\right)}+\frac{1}{x}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x}{x^{2}+5}+\frac{1}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+5 and x is x\left(x^{2}+5\right). Multiply \frac{x}{x^{2}+5} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{x^{2}+5}{x^{2}+5}.

$$\frac{xx}{x\left(x^{2}+5\right)}+\frac{x^{2}+5}{x\left(x^{2}+5\right)}$$

Since \frac{xx}{x\left(x^{2}+5\right)} and \frac{x^{2}+5}{x\left(x^{2}+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{xx+x^{2}+5}{x\left(x^{2}+5\right)}$$

Do the multiplications in xx+x^{2}+5.

$$\frac{x^{2}+x^{2}+5}{x\left(x^{2}+5\right)}$$

Combine like terms in x^{2}+x^{2}+5.

$$\frac{2x^{2}+5}{x\left(x^{2}+5\right)}$$

Expand x\left(x^{2}+5\right).

$$\frac{2x^{2}+5}{x^{3}+5x}$$

Factor

$$\frac{2x^{2}+5}{x\left(x^{2}+5\right)}$$