Question

simplify please it is urgent ​

Answer 1

Solution :-

Given

$\dfrac{7}{20} + \dfrac{17}{-45} + \dfrac{-11}{-13} + \dfrac{-8}{15}$

$= \dfrac{7}{20} + \dfrac{-17}{45} + \dfrac{11}{13} + \dfrac{-8}{15}$

Now we have to find out the

LCM of 20 , 45 , 13 , 15

20 = 2² × 5

45 = 3² × 5

13 = 13 × 1

15 = 3 × 5

So LCM of 20 , 45 , 13 , 15

= 2² × 3² × 13 × 5

= 4 × 9 × 13 × 5

= 2340

Now as

20 × 117 = 2340

Then $\dfrac{7}{20} = \dfrac{819}{2340}$

45 × 52 = 2340

Then $\dfrac{-17}{45} = \dfrac{-884}{2340}$

13 × 180 = 2340

Then $\dfrac{11}{13} = \dfrac{1980}{2340}$

15 × 156 = 2340

Then $\dfrac{-8}{15} = \dfrac{-1248}{2340}$

So now sum

$= \dfrac{819}{2340} + \dfrac{-884}{2340} + \dfrac{1980}{2340} + \dfrac{-1248}{2340}$

$= \dfrac{819 - 884}{2340} + \dfrac{1980 - 1248}{2340}$

$= \dfrac{-65}{2340} + \dfrac{732}{2340}$

$= \dfrac{667}{2340}$