Solve 1/n-1/n^2/frac{1{n^4}}+n/frac{1{n}}:frac{n^2}{n^2}

$$\frac { \frac { 1 } { n } - \frac { 1 } { n ^ { 2 } } } { \frac { 1 } { n ^ { 4 } } } + \frac { n } { \frac { 1 } { n } } : \frac { n ^ { 2 } } { n ^ { 2 } }$$

Evaluate

$$n^{3}$$

Solution Steps

Divide n^{2} by n^{2} to get 1.

$$\frac{\frac{1}{n}-\frac{1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

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

$$\frac{\frac{n}{n^{2}}-\frac{1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Since \frac{n}{n^{2}} and \frac{1}{n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{n-1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Divide \frac{n-1}{n^{2}} by \frac{1}{n^{4}} by multiplying \frac{n-1}{n^{2}} by the reciprocal of \frac{1}{n^{4}}.

$$\frac{\left(n-1\right)n^{4}}{n^{2}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

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

$$\left(n-1\right)n^{2}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Divide n by \frac{1}{n} by multiplying n by the reciprocal of \frac{1}{n}.

$$\left(n-1\right)n^{2}+\frac{nn}{1}$$

Multiply n and n to get n^{2}.

$$\left(n-1\right)n^{2}+\frac{n^{2}}{1}$$

Anything divided by one gives itself.

$$\left(n-1\right)n^{2}+n^{2}$$

Use the distributive property to multiply n-1 by n^{2}.

$$n^{3}-n^{2}+n^{2}$$

Combine -n^{2} and n^{2} to get 0.

$$n^{3}$$

Expand

$$n^{3}$$

Solution Steps

Divide n^{2} by n^{2} to get 1.

$$\frac{\frac{1}{n}-\frac{1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

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

$$\frac{\frac{n}{n^{2}}-\frac{1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Since \frac{n}{n^{2}} and \frac{1}{n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{n-1}{n^{2}}}{\frac{1}{n^{4}}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Divide \frac{n-1}{n^{2}} by \frac{1}{n^{4}} by multiplying \frac{n-1}{n^{2}} by the reciprocal of \frac{1}{n^{4}}.

$$\frac{\left(n-1\right)n^{4}}{n^{2}}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

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

$$\left(n-1\right)n^{2}+\frac{\frac{n}{\frac{1}{n}}}{1}$$

Divide n by \frac{1}{n} by multiplying n by the reciprocal of \frac{1}{n}.

$$\left(n-1\right)n^{2}+\frac{nn}{1}$$

Multiply n and n to get n^{2}.

$$\left(n-1\right)n^{2}+\frac{n^{2}}{1}$$

Anything divided by one gives itself.

$$\left(n-1\right)n^{2}+n^{2}$$

Use the distributive property to multiply n-1 by n^{2}.

$$n^{3}-n^{2}+n^{2}$$

Combine -n^{2} and n^{2} to get 0.

$$n^{3}$$