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

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

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Add 1 and 1 to get 2.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

$$\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3}{2}}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

$$\frac{1}{1+\frac{1}{1+1\times \frac{2}{3}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{1}{1+\frac{1}{1+\frac{2}{3}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

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

$$\frac{1}{1+\frac{1}{\frac{3}{3}+\frac{2}{3}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{1}{\frac{3+2}{3}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Add 3 and 2 to get 5.

$$\frac{1}{1+\frac{1}{\frac{5}{3}}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Divide 1 by \frac{5}{3} by multiplying 1 by the reciprocal of \frac{5}{3}.

$$\frac{1}{1+1\times \frac{3}{5}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{1}{1+\frac{1}{1+1}}\right)}$$

Add 1 and 1 to get 2.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{1}{1+\frac{1}{2}}\right)}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{1}{\frac{2}{2}+\frac{1}{2}}\right)}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{1}{\frac{2+1}{2}}\right)}$$

Add 2 and 1 to get 3.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{1}{\frac{3}{2}}\right)}$$

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

$$\frac{1}{1+\frac{3}{5}\left(-1+1\times \frac{2}{3}\right)}$$

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{1}{1+\frac{3}{5}\left(-1+\frac{2}{3}\right)}$$

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

$$\frac{1}{1+\frac{3}{5}\left(-\frac{3}{3}+\frac{2}{3}\right)}$$

Since -\frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{1+\frac{3}{5}\times \frac{-3+2}{3}}$$

Add -3 and 2 to get -1.

$$\frac{1}{1+\frac{3}{5}\left(-\frac{1}{3}\right)}$$

Multiply \frac{3}{5} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{1+\frac{3\left(-1\right)}{5\times 3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{1+\frac{-1}{5}}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$\frac{1}{1-\frac{1}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{1}{\frac{5}{5}-\frac{1}{5}}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{5-1}{5}}$$

Subtract 1 from 5 to get 4.

$$\frac{1}{\frac{4}{5}}$$

Divide 1 by \frac{4}{5} by multiplying 1 by the reciprocal of \frac{4}{5}.

$$1\times \frac{5}{4}$$

Multiply 1 and \frac{5}{4} to get \frac{5}{4}.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$