Solve 1/2004*2005+1/(2004+1)*(2005+1)

$$\frac{ 1 }{ 2004 \times 2005 } + \frac{ 1 }{ (2004+1) \times (2005+1) }$$

Evaluate

$$\frac{1}{2010012}\approx 0.000000498$$

Solution Steps

Multiply 2004 and 2005 to get 4018020.

$$\frac{1}{4018020}+\frac{1}{\left(2004+1\right)\left(2005+1\right)}$$

Add 2004 and 1 to get 2005.

$$\frac{1}{4018020}+\frac{1}{2005\left(2005+1\right)}$$

Add 2005 and 1 to get 2006.

$$\frac{1}{4018020}+\frac{1}{2005\times 2006}$$

Multiply 2005 and 2006 to get 4022030.

$$\frac{1}{4018020}+\frac{1}{4022030}$$

Least common multiple of 4018020 and 4022030 is 4030074060. Convert \frac{1}{4018020} and \frac{1}{4022030} to fractions with denominator 4030074060.

$$\frac{1003}{4030074060}+\frac{1002}{4030074060}$$

Since \frac{1003}{4030074060} and \frac{1002}{4030074060} have the same denominator, add them by adding their numerators.

$$\frac{1003+1002}{4030074060}$$

Add 1003 and 1002 to get 2005.

$$\frac{2005}{4030074060}$$

Reduce the fraction \frac{2005}{4030074060} to lowest terms by extracting and canceling out 2005.

$$\frac{1}{2010012}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 \cdot 17 \cdot 59 \cdot 167} = 4.975094676051686 \times 10^{-7}$$