Solve (621/126+739/358+458/947)*(739/358+frac{458}{947}+frac{378}{207})-(frac{621}{126}+frac{739}{358}+frac{458}{947}+frac{378}{207})*(frac{739}{358}+frac{458}{947})

$$( \frac { 621 } { 126 } + \frac { 739 } { 358 } + \frac { 458 } { 947 } ) \times ( \frac { 739 } { 358 } + \frac { 458 } { 947 } + \frac { 378 } { 207 } ) - ( \frac { 621 } { 126 } + \frac { 739 } { 358 } + \frac { 458 } { 947 } + \frac { 378 } { 207 } ) \times ( \frac { 739 } { 358 } + \frac { 458 } { 947 } )$$

Evaluate

$$9$$

Solution Steps

Reduce the fraction \frac{621}{126} to lowest terms by extracting and canceling out 9.

$$\left(\frac{69}{14}+\frac{739}{358}+\frac{458}{947}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 14 and 358 is 2506. Convert \frac{69}{14} and \frac{739}{358} to fractions with denominator 2506.

$$\left(\frac{12351}{2506}+\frac{5173}{2506}+\frac{458}{947}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{12351}{2506} and \frac{5173}{2506} have the same denominator, add them by adding their numerators.

$$\left(\frac{12351+5173}{2506}+\frac{458}{947}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 12351 and 5173 to get 17524.

$$\left(\frac{17524}{2506}+\frac{458}{947}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{17524}{2506} to lowest terms by extracting and canceling out 2.

$$\left(\frac{8762}{1253}+\frac{458}{947}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 1253 and 947 is 1186591. Convert \frac{8762}{1253} and \frac{458}{947} to fractions with denominator 1186591.

$$\left(\frac{8297614}{1186591}+\frac{573874}{1186591}\right)\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{8297614}{1186591} and \frac{573874}{1186591} have the same denominator, add them by adding their numerators.

$$\frac{8297614+573874}{1186591}\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 8297614 and 573874 to get 8871488.

$$\frac{8871488}{1186591}\left(\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 358 and 947 is 339026. Convert \frac{739}{358} and \frac{458}{947} to fractions with denominator 339026.

$$\frac{8871488}{1186591}\left(\frac{699833}{339026}+\frac{163964}{339026}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{699833}{339026} and \frac{163964}{339026} have the same denominator, add them by adding their numerators.

$$\frac{8871488}{1186591}\left(\frac{699833+163964}{339026}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 699833 and 163964 to get 863797.

$$\frac{8871488}{1186591}\left(\frac{863797}{339026}+\frac{378}{207}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{378}{207} to lowest terms by extracting and canceling out 9.

$$\frac{8871488}{1186591}\left(\frac{863797}{339026}+\frac{42}{23}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 339026 and 23 is 7797598. Convert \frac{863797}{339026} and \frac{42}{23} to fractions with denominator 7797598.

$$\frac{8871488}{1186591}\left(\frac{19867331}{7797598}+\frac{14239092}{7797598}\right)-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{19867331}{7797598} and \frac{14239092}{7797598} have the same denominator, add them by adding their numerators.

$$\frac{8871488}{1186591}\times \frac{19867331+14239092}{7797598}-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 19867331 and 14239092 to get 34106423.

$$\frac{8871488}{1186591}\times \frac{34106423}{7797598}-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Multiply \frac{8871488}{1186591} times \frac{34106423}{7797598} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8871488\times 34106423}{1186591\times 7797598}-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Do the multiplications in the fraction \frac{8871488\times 34106423}{1186591\times 7797598}.

$$\frac{302574722367424}{9252559608418}-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{302574722367424}{9252559608418} to lowest terms by extracting and canceling out 2.

$$\frac{151287361183712}{4626279804209}-\left(\frac{621}{126}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{621}{126} to lowest terms by extracting and canceling out 9.

$$\frac{151287361183712}{4626279804209}-\left(\frac{69}{14}+\frac{739}{358}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 14 and 358 is 2506. Convert \frac{69}{14} and \frac{739}{358} to fractions with denominator 2506.

$$\frac{151287361183712}{4626279804209}-\left(\frac{12351}{2506}+\frac{5173}{2506}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{12351}{2506} and \frac{5173}{2506} have the same denominator, add them by adding their numerators.

$$\frac{151287361183712}{4626279804209}-\left(\frac{12351+5173}{2506}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 12351 and 5173 to get 17524.

$$\frac{151287361183712}{4626279804209}-\left(\frac{17524}{2506}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{17524}{2506} to lowest terms by extracting and canceling out 2.

$$\frac{151287361183712}{4626279804209}-\left(\frac{8762}{1253}+\frac{458}{947}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 1253 and 947 is 1186591. Convert \frac{8762}{1253} and \frac{458}{947} to fractions with denominator 1186591.

$$\frac{151287361183712}{4626279804209}-\left(\frac{8297614}{1186591}+\frac{573874}{1186591}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{8297614}{1186591} and \frac{573874}{1186591} have the same denominator, add them by adding their numerators.

$$\frac{151287361183712}{4626279804209}-\left(\frac{8297614+573874}{1186591}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 8297614 and 573874 to get 8871488.

$$\frac{151287361183712}{4626279804209}-\left(\frac{8871488}{1186591}+\frac{378}{207}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Reduce the fraction \frac{378}{207} to lowest terms by extracting and canceling out 9.

$$\frac{151287361183712}{4626279804209}-\left(\frac{8871488}{1186591}+\frac{42}{23}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 1186591 and 23 is 27291593. Convert \frac{8871488}{1186591} and \frac{42}{23} to fractions with denominator 27291593.

$$\frac{151287361183712}{4626279804209}-\left(\frac{204044224}{27291593}+\frac{49836822}{27291593}\right)\left(\frac{739}{358}+\frac{458}{947}\right)$$

Since \frac{204044224}{27291593} and \frac{49836822}{27291593} have the same denominator, add them by adding their numerators.

$$\frac{151287361183712}{4626279804209}-\frac{204044224+49836822}{27291593}\left(\frac{739}{358}+\frac{458}{947}\right)$$

Add 204044224 and 49836822 to get 253881046.

$$\frac{151287361183712}{4626279804209}-\frac{253881046}{27291593}\left(\frac{739}{358}+\frac{458}{947}\right)$$

Least common multiple of 358 and 947 is 339026. Convert \frac{739}{358} and \frac{458}{947} to fractions with denominator 339026.

$$\frac{151287361183712}{4626279804209}-\frac{253881046}{27291593}\left(\frac{699833}{339026}+\frac{163964}{339026}\right)$$

Since \frac{699833}{339026} and \frac{163964}{339026} have the same denominator, add them by adding their numerators.

$$\frac{151287361183712}{4626279804209}-\frac{253881046}{27291593}\times \frac{699833+163964}{339026}$$

Add 699833 and 163964 to get 863797.

$$\frac{151287361183712}{4626279804209}-\frac{253881046}{27291593}\times \frac{863797}{339026}$$

Multiply \frac{253881046}{27291593} times \frac{863797}{339026} by multiplying numerator times numerator and denominator times denominator.

$$\frac{151287361183712}{4626279804209}-\frac{253881046\times 863797}{27291593\times 339026}$$

Do the multiplications in the fraction \frac{253881046\times 863797}{27291593\times 339026}.

$$\frac{151287361183712}{4626279804209}-\frac{219301685891662}{9252559608418}$$

Reduce the fraction \frac{219301685891662}{9252559608418} to lowest terms by extracting and canceling out 2.

$$\frac{151287361183712}{4626279804209}-\frac{109650842945831}{4626279804209}$$

Since \frac{151287361183712}{4626279804209} and \frac{109650842945831}{4626279804209} have the same denominator, subtract them by subtracting their numerators.

$$\frac{151287361183712-109650842945831}{4626279804209}$$

Subtract 109650842945831 from 151287361183712 to get 41636518237881.

$$\frac{41636518237881}{4626279804209}$$

Divide 41636518237881 by 4626279804209 to get 9.

$$9$$

Factor

$$3^{2}$$