Solve 1/frac{145{1728}-1}

$$\frac{ 1 }{ \frac{ 145 }{ 1728 } -1 }$$

Evaluate

$$-\frac{1728}{1583}\approx -1.091598231$$

Solution Steps

Convert 1 to fraction \frac{1728}{1728}.

$$\frac{1}{\frac{145}{1728}-\frac{1728}{1728}}$$

Since \frac{145}{1728} and \frac{1728}{1728} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{145-1728}{1728}}$$

Subtract 1728 from 145 to get -1583.

$$\frac{1}{-\frac{1583}{1728}}$$

Divide 1 by -\frac{1583}{1728} by multiplying 1 by the reciprocal of -\frac{1583}{1728}.

$$1\left(-\frac{1728}{1583}\right)$$

Multiply 1 and -\frac{1728}{1583} to get -\frac{1728}{1583}.

$$-\frac{1728}{1583}$$

Factor

$$-\frac{1728}{1583} = -1\frac{145}{1583} = -1.0915982312065697$$