Solve 1/x+4/x^2/x+frac{64{x^2}}

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

Evaluate

$$\frac{1}{x^{2}-4x+16}$$

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in xx^{2}+64.

$$\frac{\frac{x+4}{x^{2}}}{\frac{x^{3}+64}{x^{2}}}$$

Divide \frac{x+4}{x^{2}} by \frac{x^{3}+64}{x^{2}} by multiplying \frac{x+4}{x^{2}} by the reciprocal of \frac{x^{3}+64}{x^{2}}.

$$\frac{\left(x+4\right)x^{2}}{x^{2}\left(x^{3}+64\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x+4}{x^{3}+64}$$

Factor the expressions that are not already factored.

$$\frac{x+4}{\left(x+4\right)\left(x^{2}-4x+16\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{1}{x^{2}-4x+16}$$

Expand

$$\frac{1}{x^{2}-4x+16}$$

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in xx^{2}+64.

$$\frac{\frac{x+4}{x^{2}}}{\frac{x^{3}+64}{x^{2}}}$$

Divide \frac{x+4}{x^{2}} by \frac{x^{3}+64}{x^{2}} by multiplying \frac{x+4}{x^{2}} by the reciprocal of \frac{x^{3}+64}{x^{2}}.

$$\frac{\left(x+4\right)x^{2}}{x^{2}\left(x^{3}+64\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x+4}{x^{3}+64}$$

Factor the expressions that are not already factored.

$$\frac{x+4}{\left(x+4\right)\left(x^{2}-4x+16\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{1}{x^{2}-4x+16}$$