Solve 0.999^2-1/0.999-1

$$\frac{ { 0.999 }^{ 2 } -1 }{ 0.999-1 }$$

Evaluate

$$1.999$$

Solution Steps

Calculate 0.999 to the power of 2 and get 0.998001.

$$\frac{0.998001-1}{0.999-1}$$

Subtract 1 from 0.998001 to get -0.001999.

$$\frac{-0.001999}{0.999-1}$$

Subtract 1 from 0.999 to get -0.001.

$$\frac{-0.001999}{-0.001}$$

Expand \frac{-0.001999}{-0.001} by multiplying both numerator and the denominator by 1000000.

$$\frac{-1999}{-1000}$$

Fraction \frac{-1999}{-1000} can be simplified to \frac{1999}{1000} by removing the negative sign from both the numerator and the denominator.

$$\frac{1999}{1000}$$

Factor

$$\frac{1999}{2 ^ {3} \cdot 5 ^ {3}} = 1\frac{999}{1000} = 1.999$$