Solve 1/1-1{1+frac{1/3}}

$$\frac{ 1 }{ 1- \frac{ 1 }{ 1+ \frac{ 1 }{ 3 } } }$$

Evaluate

$$4$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{1-\frac{1}{\frac{3}{3}+\frac{1}{3}}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{1-\frac{1}{\frac{3+1}{3}}}$$

Add 3 and 1 to get 4.

$$\frac{1}{1-\frac{1}{\frac{4}{3}}}$$

Divide 1 by \frac{4}{3} by multiplying 1 by the reciprocal of \frac{4}{3}.

$$\frac{1}{1-1\times \frac{3}{4}}$$

Multiply 1 and \frac{3}{4} to get \frac{3}{4}.

$$\frac{1}{1-\frac{3}{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{\frac{4}{4}-\frac{3}{4}}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{4-3}{4}}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{\frac{1}{4}}$$

Divide 1 by \frac{1}{4} by multiplying 1 by the reciprocal of \frac{1}{4}.

$$1\times 4$$

Multiply 1 and 4 to get 4.

$$4$$

Factor

$$2^{2}$$