Solve 2015div20152015/2016+2018+1/2017/2017+frac{1{2018}}=

$$2015 \div 2015 \frac { 2015 } { 2016 } + \frac { 2018 + \frac { 1 } { 2017 } } { 2017 + \frac { 1 } { 2018 } } =$$

Evaluate

$$2$$

Solution Steps

Divide 2015 by \frac{2015\times 2016+2015}{2016} by multiplying 2015 by the reciprocal of \frac{2015\times 2016+2015}{2016}.

$$\frac{2015\times 2016}{2015\times 2016+2015}+\frac{2018+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Multiply 2015 and 2016 to get 4062240.

$$\frac{4062240}{2015\times 2016+2015}+\frac{2018+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Multiply 2015 and 2016 to get 4062240.

$$\frac{4062240}{4062240+2015}+\frac{2018+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Add 4062240 and 2015 to get 4064255.

$$\frac{4062240}{4064255}+\frac{2018+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Reduce the fraction \frac{4062240}{4064255} to lowest terms by extracting and canceling out 2015.

$$\frac{2016}{2017}+\frac{2018+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Convert 2018 to fraction \frac{4070306}{2017}.

$$\frac{2016}{2017}+\frac{\frac{4070306}{2017}+\frac{1}{2017}}{2017+\frac{1}{2018}}$$

Since \frac{4070306}{2017} and \frac{1}{2017} have the same denominator, add them by adding their numerators.

$$\frac{2016}{2017}+\frac{\frac{4070306+1}{2017}}{2017+\frac{1}{2018}}$$

Add 4070306 and 1 to get 4070307.

$$\frac{2016}{2017}+\frac{\frac{4070307}{2017}}{2017+\frac{1}{2018}}$$

Convert 2017 to fraction \frac{4070306}{2018}.

$$\frac{2016}{2017}+\frac{\frac{4070307}{2017}}{\frac{4070306}{2018}+\frac{1}{2018}}$$

Since \frac{4070306}{2018} and \frac{1}{2018} have the same denominator, add them by adding their numerators.

$$\frac{2016}{2017}+\frac{\frac{4070307}{2017}}{\frac{4070306+1}{2018}}$$

Add 4070306 and 1 to get 4070307.

$$\frac{2016}{2017}+\frac{\frac{4070307}{2017}}{\frac{4070307}{2018}}$$

Divide \frac{4070307}{2017} by \frac{4070307}{2018} by multiplying \frac{4070307}{2017} by the reciprocal of \frac{4070307}{2018}.

$$\frac{2016}{2017}+\frac{4070307}{2017}\times \frac{2018}{4070307}$$

Multiply \frac{4070307}{2017} times \frac{2018}{4070307} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2016}{2017}+\frac{4070307\times 2018}{2017\times 4070307}$$

Cancel out 4070307 in both numerator and denominator.

$$\frac{2016}{2017}+\frac{2018}{2017}$$

Since \frac{2016}{2017} and \frac{2018}{2017} have the same denominator, add them by adding their numerators.

$$\frac{2016+2018}{2017}$$

Add 2016 and 2018 to get 4034.

$$\frac{4034}{2017}$$

Divide 4034 by 2017 to get 2.

$$2$$

Factor

$$2$$