Solve 2017div20172017/2018+2017*(43*87+44)/44*87-43

$$2017 \div 2017 \frac { 2017 } { 2018 } + \frac { 2017 \times ( 43 \times 87 + 44 ) } { 44 \times 87 - 43 }$$

Evaluate

$$\frac{4074341}{2019}\approx 2017.999504705$$

Solution Steps

Divide 2017 by \frac{2017\times 2018+2017}{2018} by multiplying 2017 by the reciprocal of \frac{2017\times 2018+2017}{2018}.

$$\frac{2017\times 2018}{2017\times 2018+2017}+\frac{2017\left(43\times 87+44\right)}{44\times 87-43}$$

Multiply 2017 and 2018 to get 4070306.

$$\frac{4070306}{2017\times 2018+2017}+\frac{2017\left(43\times 87+44\right)}{44\times 87-43}$$

Multiply 2017 and 2018 to get 4070306.

$$\frac{4070306}{4070306+2017}+\frac{2017\left(43\times 87+44\right)}{44\times 87-43}$$

Add 4070306 and 2017 to get 4072323.

$$\frac{4070306}{4072323}+\frac{2017\left(43\times 87+44\right)}{44\times 87-43}$$

Reduce the fraction \frac{4070306}{4072323} to lowest terms by extracting and canceling out 2017.

$$\frac{2018}{2019}+\frac{2017\left(43\times 87+44\right)}{44\times 87-43}$$

Multiply 43 and 87 to get 3741.

$$\frac{2018}{2019}+\frac{2017\left(3741+44\right)}{44\times 87-43}$$

Add 3741 and 44 to get 3785.

$$\frac{2018}{2019}+\frac{2017\times 3785}{44\times 87-43}$$

Multiply 2017 and 3785 to get 7634345.

$$\frac{2018}{2019}+\frac{7634345}{44\times 87-43}$$

Multiply 44 and 87 to get 3828.

$$\frac{2018}{2019}+\frac{7634345}{3828-43}$$

Subtract 43 from 3828 to get 3785.

$$\frac{2018}{2019}+\frac{7634345}{3785}$$

Divide 7634345 by 3785 to get 2017.

$$\frac{2018}{2019}+2017$$

Convert 2017 to fraction \frac{4072323}{2019}.

$$\frac{2018}{2019}+\frac{4072323}{2019}$$

Since \frac{2018}{2019} and \frac{4072323}{2019} have the same denominator, add them by adding their numerators.

$$\frac{2018+4072323}{2019}$$

Add 2018 and 4072323 to get 4074341.

$$\frac{4074341}{2019}$$

Factor

$$\frac{19 \cdot 214439}{3 \cdot 673} = 2017\frac{2018}{2019} = 2017.9995047052996$$