Solve -(+9/41)-(-13/14)+9/41+(-13/14)

$$-(+ \frac{ 9 }{ 41 } )-(- \frac{ 13 }{ 14 } )+ \frac{ 9 }{ 41 } +(- \frac{ 13 }{ 14 } )$$

Evaluate

$$0$$

Solution Steps

The opposite of -\frac{13}{14} is \frac{13}{14}.

$$-\frac{9}{41}+\frac{13}{14}+\frac{9}{41}-\frac{13}{14}$$

Least common multiple of 41 and 14 is 574. Convert -\frac{9}{41} and \frac{13}{14} to fractions with denominator 574.

$$-\frac{126}{574}+\frac{533}{574}+\frac{9}{41}-\frac{13}{14}$$

Since -\frac{126}{574} and \frac{533}{574} have the same denominator, add them by adding their numerators.

$$\frac{-126+533}{574}+\frac{9}{41}-\frac{13}{14}$$

Add -126 and 533 to get 407.

$$\frac{407}{574}+\frac{9}{41}-\frac{13}{14}$$

Least common multiple of 574 and 41 is 574. Convert \frac{407}{574} and \frac{9}{41} to fractions with denominator 574.

$$\frac{407}{574}+\frac{126}{574}-\frac{13}{14}$$

Since \frac{407}{574} and \frac{126}{574} have the same denominator, add them by adding their numerators.

$$\frac{407+126}{574}-\frac{13}{14}$$

Add 407 and 126 to get 533.

$$\frac{533}{574}-\frac{13}{14}$$

Reduce the fraction \frac{533}{574} to lowest terms by extracting and canceling out 41.

$$\frac{13}{14}-\frac{13}{14}$$

Subtract \frac{13}{14} from \frac{13}{14} to get 0.

$$0$$

Factor

$$0$$