Answer:
(-74)/15
Step-by-step explanation:
Simplify the following:
(1 + 5/9)/((-2)/3) - (2 + 3/5)
Multiply the numerator of (1 + 5/9)/((-2)/3) by the reciprocal of the denominator. (1 + 5/9)/((-2)/3) = ((1 + 5/9)×3)/(-2):
((5/9 + 1) 3)/(-2) - (2 + 3/5)
Put 1 + 5/9 over the common denominator 9. 1 + 5/9 = 9/9 + 5/9:
(9/9 + 5/9 3)/(-2) - (2 + 3/5)
9/9 + 5/9 = (9 + 5)/9:
((9 + 5)/9×3)/(-2) - (2 + 3/5)
9 + 5 = 14:
(14/9×3)/(-2) - (2 + 3/5)
14/9×3 = (14×3)/9:
((14×3)/9)/(-2) - (2 + 3/5)
((14×3)/9)/(-2) = (14×3)/(9 (-2)):
(14×3)/(9 (-2)) - (2 + 3/5)
3/9 = 3/(3×3) = 1/3:
14/(3 (-2)) - (2 + 3/5)
The gcd of 14 and -2 is 2, so 14/(3 (-2)) = (2×7)/(3 (2 (-1))) = 2/2×7/(3 (-1)) = 7/(3 (-1)):
7/(3×-1) - (2 + 3/5)
Put 2 + 3/5 over the common denominator 5. 2 + 3/5 = (5×2)/5 + 3/5:
7/(-3) - (5×2)/5 + 3/5
5×2 = 10:
7/(-3) - (10/5 + 3/5)
10/5 + 3/5 = (10 + 3)/5:
7/(-3) - (10 + 3)/5
10 + 3 = 13:
7/(-3) - 13/5
Multiply numerator and denominator of 7/(-3) by -1:
(-7)/3 - 13/5
Put (-7)/3 - 13/5 over the common denominator 15. (-7)/3 - 13/5 = (5 (-7))/15 + (3 (-13))/15:
(5 (-7))/15 + (3 (-13))/15
5 (-7) = -35:
(-35)/15 + (3 (-13))/15
3 (-13) = -39:
(-35)/15 + (-39)/15
-35/15 - 39/15 = (-35 - 39)/15:
(-35 - 39)/15
-35 - 39 = -(35 + 39):
(-(35 + 39))/15
| 1 |
| 3 | 9
+ | 3 | 5
| 7 | 4:
Answer: (-74)/15
