Solve 1997/1997frac{1997{1998}}+1/1999

$$\frac{ 1997 }{ 1997 \frac{ 1997 }{ 1998 } } + \frac{ 1 }{ 1999 }$$

Evaluate

$$1$$

Solution Steps

Divide 1997 by \frac{1997\times 1998+1997}{1998} by multiplying 1997 by the reciprocal of \frac{1997\times 1998+1997}{1998}.

$$\frac{1997\times 1998}{1997\times 1998+1997}+\frac{1}{1999}$$

Multiply 1997 and 1998 to get 3990006.

$$\frac{3990006}{1997\times 1998+1997}+\frac{1}{1999}$$

Multiply 1997 and 1998 to get 3990006.

$$\frac{3990006}{3990006+1997}+\frac{1}{1999}$$

Add 3990006 and 1997 to get 3992003.

$$\frac{3990006}{3992003}+\frac{1}{1999}$$

Reduce the fraction \frac{3990006}{3992003} to lowest terms by extracting and canceling out 1997.

$$\frac{1998}{1999}+\frac{1}{1999}$$

Since \frac{1998}{1999} and \frac{1}{1999} have the same denominator, add them by adding their numerators.

$$\frac{1998+1}{1999}$$

Add 1998 and 1 to get 1999.

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

Divide 1999 by 1999 to get 1.

$$1$$

Factor

$$1$$