Solve 5/x^2+x^2/5/frac{5{x}}

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

Evaluate

$$\frac{x^{3}}{25}+\frac{1}{x}$$

Short Solution Steps

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

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

Since \frac{5\times 5}{5x^{2}} and \frac{x^{2}x^{2}}{5x^{2}} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{25+x^{4}}{5x^{2}}}{\frac{5}{x}}$$

Divide \frac{25+x^{4}}{5x^{2}} by \frac{5}{x} by multiplying \frac{25+x^{4}}{5x^{2}} by the reciprocal of \frac{5}{x}.

$$\frac{\left(25+x^{4}\right)x}{5x^{2}\times 5}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{4}+25}{5\times 5x}$$

Multiply 5 and 5 to get 25.

$$\frac{x^{4}+25}{25x}$$

Expand

$$\frac{x^{3}}{25}+\frac{1}{x}$$

Short Solution Steps

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

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

Since \frac{5\times 5}{5x^{2}} and \frac{x^{2}x^{2}}{5x^{2}} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{25+x^{4}}{5x^{2}}}{\frac{5}{x}}$$

Divide \frac{25+x^{4}}{5x^{2}} by \frac{5}{x} by multiplying \frac{25+x^{4}}{5x^{2}} by the reciprocal of \frac{5}{x}.

$$\frac{\left(25+x^{4}\right)x}{5x^{2}\times 5}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{4}+25}{5\times 5x}$$

Multiply 5 and 5 to get 25.

$$\frac{x^{4}+25}{25x}$$