Solve x=2+frac{1/3frac{4{5}}}{2+1/3+1{1+frac{1/4}}}

$$x = \frac { 2 + \frac { 1 } { 3 \frac { 4 } { 5 } } } { 2 + \frac { 1 } { 3 + \frac { 1 } { 1 + \frac { 1 } { 4 } } } }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Divide 1 by \frac{3\times 5+4}{5} by multiplying 1 by the reciprocal of \frac{3\times 5+4}{5}.

$$x=\frac{2+\frac{5}{3\times 5+4}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Multiply 3 and 5 to get 15.

$$x=\frac{2+\frac{5}{15+4}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Add 15 and 4 to get 19.

$$x=\frac{2+\frac{5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Convert 2 to fraction \frac{38}{19}.

$$x=\frac{\frac{38}{19}+\frac{5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Since \frac{38}{19} and \frac{5}{19} have the same denominator, add them by adding their numerators.

$$x=\frac{\frac{38+5}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

Add 38 and 5 to get 43.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{1+\frac{1}{4}}}}$$

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

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{4}{4}+\frac{1}{4}}}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{4+1}{4}}}}$$

Add 4 and 1 to get 5.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{1}{\frac{5}{4}}}}$$

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

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+1\times \frac{4}{5}}}$$

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

$$x=\frac{\frac{43}{19}}{2+\frac{1}{3+\frac{4}{5}}}$$

Convert 3 to fraction \frac{15}{5}.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{15}{5}+\frac{4}{5}}}$$

Since \frac{15}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{15+4}{5}}}$$

Add 15 and 4 to get 19.

$$x=\frac{\frac{43}{19}}{2+\frac{1}{\frac{19}{5}}}$$

Divide 1 by \frac{19}{5} by multiplying 1 by the reciprocal of \frac{19}{5}.

$$x=\frac{\frac{43}{19}}{2+1\times \frac{5}{19}}$$

Multiply 1 and \frac{5}{19} to get \frac{5}{19}.

$$x=\frac{\frac{43}{19}}{2+\frac{5}{19}}$$

Convert 2 to fraction \frac{38}{19}.

$$x=\frac{\frac{43}{19}}{\frac{38}{19}+\frac{5}{19}}$$

Since \frac{38}{19} and \frac{5}{19} have the same denominator, add them by adding their numerators.

$$x=\frac{\frac{43}{19}}{\frac{38+5}{19}}$$

Add 38 and 5 to get 43.

$$x=\frac{\frac{43}{19}}{\frac{43}{19}}$$

Divide \frac{43}{19} by \frac{43}{19} to get 1.

$$x=1$$

Assign x

$$x≔1$$