Solve 2017div20172017/2018+2017*(4.3*87+4.4)/4.4*87-4.3

$$2017 \div 2017 \frac { 2017 } { 2018 } + \frac { 2017 \times ( 4.3 \times 87 + 4.4 ) } { 4.4 \times 87 - 4.3 }$$

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}.

$$\frac{2017\times 2018}{2017\times 2018+2017}+\frac{2017\left(4.3\times 87+4.4\right)}{4.4\times 87-4.3}$$

Multiply 2017 and 2018 to get 4070306.

$$\frac{4070306}{2017\times 2018+2017}+\frac{2017\left(4.3\times 87+4.4\right)}{4.4\times 87-4.3}$$

Multiply 2017 and 2018 to get 4070306.

$$\frac{4070306}{4070306+2017}+\frac{2017\left(4.3\times 87+4.4\right)}{4.4\times 87-4.3}$$

Add 4070306 and 2017 to get 4072323.

$$\frac{4070306}{4072323}+\frac{2017\left(4.3\times 87+4.4\right)}{4.4\times 87-4.3}$$

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

$$\frac{2018}{2019}+\frac{2017\left(4.3\times 87+4.4\right)}{4.4\times 87-4.3}$$

Multiply 4.3 and 87 to get 374.1.

$$\frac{2018}{2019}+\frac{2017\left(374.1+4.4\right)}{4.4\times 87-4.3}$$

Add 374.1 and 4.4 to get 378.5.

$$\frac{2018}{2019}+\frac{2017\times 378.5}{4.4\times 87-4.3}$$

Multiply 2017 and 378.5 to get 763434.5.

$$\frac{2018}{2019}+\frac{763434.5}{4.4\times 87-4.3}$$

Multiply 4.4 and 87 to get 382.8.

$$\frac{2018}{2019}+\frac{763434.5}{382.8-4.3}$$

Subtract 4.3 from 382.8 to get 378.5.

$$\frac{2018}{2019}+\frac{763434.5}{378.5}$$

Expand \frac{763434.5}{378.5} by multiplying both numerator and the denominator by 10.

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

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

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