Solve 3/1-1{?+frac{1/1+frac{1{5}}}}=69/17

$$\frac { 3 } { 1 - \frac { 1 } { ? + \frac { 1 } { 1 + \frac { 1 } { 5 } } } } = \frac { 69 } { 17 }$$

Verify

Solution Steps

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

$$\frac{3}{1-\left(1+\frac{1}{5}\right)}=\frac{69}{17}$$

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

$$\frac{3}{1-\left(\frac{5}{5}+\frac{1}{5}\right)}=\frac{69}{17}$$

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

$$\frac{3}{1-\frac{5+1}{5}}=\frac{69}{17}$$

Add 5 and 1 to get 6.

$$\frac{3}{1-\frac{6}{5}}=\frac{69}{17}$$

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

$$\frac{3}{\frac{5}{5}-\frac{6}{5}}=\frac{69}{17}$$

Since \frac{5}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{\frac{5-6}{5}}=\frac{69}{17}$$

Subtract 6 from 5 to get -1.

$$\frac{3}{-\frac{1}{5}}=\frac{69}{17}$$

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

$$3\left(-5\right)=\frac{69}{17}$$

Multiply 3 and -5 to get -15.

$$-15=\frac{69}{17}$$

Convert -15 to fraction -\frac{255}{17}.

$$-\frac{255}{17}=\frac{69}{17}$$

Compare -\frac{255}{17} and \frac{69}{17}.

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