Solve 10/9{8/7{frac{6/frac{5{frac{4/frac{3{frac{2}{1}}}}}}}}}=x

$$\frac{ 10 }{ \frac{ 9 }{ \frac{ 8 }{ \frac{ 7 }{ \frac{ 6 }{ \frac{ 5 }{ \frac{ 4 }{ \frac{ 3 }{ \frac{ 2 }{ 1 } } } } } } } } } =x$$

Solve for x

$$x = \frac{256}{63} = 4\frac{4}{63} \approx 4.063492063$$

Steps for Solving Linear Equation

Divide 10 by \frac{9}{\frac{8}{\frac{7}{\frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}}}} by multiplying 10 by the reciprocal of \frac{9}{\frac{8}{\frac{7}{\frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}}}}.

$$\frac{10\times \frac{8}{\frac{7}{\frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}}}}{9}=x$$

Divide 8 by \frac{7}{\frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}} by multiplying 8 by the reciprocal of \frac{7}{\frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}}.

$$\frac{10\times \frac{8\times \frac{6}{\frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}}}{7}}{9}=x$$

Divide 6 by \frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}} by multiplying 6 by the reciprocal of \frac{5}{\frac{4}{\frac{3}{\frac{2}{1}}}}.

$$\frac{10\times \frac{8\times \frac{6\times \frac{4}{\frac{3}{\frac{2}{1}}}}{5}}{7}}{9}=x$$

Divide 4 by \frac{3}{\frac{2}{1}} by multiplying 4 by the reciprocal of \frac{3}{\frac{2}{1}}.

$$\frac{10\times \frac{8\times \frac{6\times \frac{4\times \frac{2}{1}}{3}}{5}}{7}}{9}=x$$

Anything divided by one gives itself.

$$\frac{10\times \frac{8\times \frac{6\times \frac{4\times 2}{3}}{5}}{7}}{9}=x$$

Multiply 4 and 2 to get 8.

$$\frac{10\times \frac{8\times \frac{6\times \frac{8}{3}}{5}}{7}}{9}=x$$

Express 6\times \frac{8}{3} as a single fraction.

$$\frac{10\times \frac{8\times \frac{\frac{6\times 8}{3}}{5}}{7}}{9}=x$$

Multiply 6 and 8 to get 48.

$$\frac{10\times \frac{8\times \frac{\frac{48}{3}}{5}}{7}}{9}=x$$

Divide 48 by 3 to get 16.

$$\frac{10\times \frac{8\times \frac{16}{5}}{7}}{9}=x$$

Express 8\times \frac{16}{5} as a single fraction.

$$\frac{10\times \frac{\frac{8\times 16}{5}}{7}}{9}=x$$

Multiply 8 and 16 to get 128.

$$\frac{10\times \frac{\frac{128}{5}}{7}}{9}=x$$

Express \frac{\frac{128}{5}}{7} as a single fraction.

$$\frac{10\times \frac{128}{5\times 7}}{9}=x$$

Multiply 5 and 7 to get 35.

$$\frac{10\times \frac{128}{35}}{9}=x$$

Express 10\times \frac{128}{35} as a single fraction.

$$\frac{\frac{10\times 128}{35}}{9}=x$$

Multiply 10 and 128 to get 1280.

$$\frac{\frac{1280}{35}}{9}=x$$

Reduce the fraction \frac{1280}{35} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{256}{7}}{9}=x$$

Express \frac{\frac{256}{7}}{9} as a single fraction.

$$\frac{256}{7\times 9}=x$$

Multiply 7 and 9 to get 63.

$$\frac{256}{63}=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=\frac{256}{63}$$