Simplify the following:
(15 x-35)/5-(48 x-5 y)/(6)
Put each term in (15 x-35)/5-(48 x-5 y)/6 over the common denominator 30: (15 x-35)/5-(48 x-5 y)/6 = (6 (15 x-35))/30+(5 (5 y-48 x))/30:
(6 (15 x-35))/30+(5 (5 y-48 x))/30
(6 (15 x-35))/30+(5 (5 y-48 x))/30 = (6 (15 x-35)+5 (5 y-48 x))/30:
(6 (15 x-35)+5 (5 y-48 x))/30
6 (15 x-35) = 90 x-210:
(90 x-210+5 (5 y-48 x))/30
5 (5 y-48 x) = 25 y-240 x:
(-210+90 x+25 y-240 x)/30
Grouping like terms, -210+90 x-240 x+25 y = 25 y+(90 x-240 x)-210:
(25 y+(90 x-240 x)-210)/30
90 x-240 x = -150 x:
(25 y+-150 x-210)/30
Factor 5 out of 25 y-150 x-210:
5 (5 y-30 x-42)/30
5/30 = 5/(5×6) = 1/6:
Answer: | (-42-30x+5y) / 6
Simplify the following:
(15 x-35)/5-(48 x-5 y)/(6)
Put each term in (15 x-35)/5-(48 x-5 y)/6 over the common denominator 30: (15 x-35)/5-(48 x-5 y)/6 = (6 (15 x-35))/30+(5 (5 y-48 x))/30:
(6 (15 x-35))/30+(5 (5 y-48 x))/30
(6 (15 x-35))/30+(5 (5 y-48 x))/30 = (6 (15 x-35)+5 (5 y-48 x))/30:
(6 (15 x-35)+5 (5 y-48 x))/30
6 (15 x-35) = 90 x-210:
(90 x-210+5 (5 y-48 x))/30
5 (5 y-48 x) = 25 y-240 x:
(-210+90 x+25 y-240 x)/30
Grouping like terms, -210+90 x-240 x+25 y = 25 y+(90 x-240 x)-210:
(25 y+(90 x-240 x)-210)/30
90 x-240 x = -150 x:
(25 y+-150 x-210)/30
Factor 5 out of 25 y-150 x-210:
5 (5 y-30 x-42)/30
5/30 = 5/(5×6) = 1/6:
Answer: | (-42-30x+5y) / 6
