SOLUTION: (2x-6)/21 divided by (5x-15)/12 i got (x-24)/(x-105) am i right or can i keep going?

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Question 119844: (2x-6)/21 divided by (5x-15)/12 i got (x-24)/(x-105) am i right or can i keep going?
Found 3 solutions by jim_thompson5910, ptaylor, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x-6%29%2F21%29%2F%28%285x-15%29%2F12%29 Start with the given expression

%28%282x-6%29%2F%2821%29%29%28%2812%29%2F%285x-15%29%29 Multiply the first fraction by the reciprocal of the second

%28%282%28x-3%29%29%2F%2821%29%29%28%2812%29%2F%285x-15%29%29 Factor 2x-6 to get 2%28x-3%29

%28%282%28x-3%29%29%2F%283%2A7%29%29%28%2812%29%2F%285x-15%29%29 Factor 21 to get 3%2A7

%28%282%28x-3%29%29%2F%283%2A7%29%29%28%283%2A4%29%2F%285x-15%29%29 Factor 12 to get 3%2A4

%28%282%28x-3%29%29%2F%283%2A7%29%29%28%283%2A4%29%2F%285%28x-3%29%29%29 Factor 5x-15 to get 5%28x-3%29


2%28x-3%29%283%2A4%29%2F%283%2A7%2A5%28x-3%29%29 Combine the fractions


2cross%28%28x-3%29%29%28cross%283%29%2A4%29%2F%28cross%283%29%2A7%2A5cross%28%28x-3%29%29%29 Combine the fractions



%282%2A4%29%2F%287%2A5%29 Cancel like terms



8%2F35 Multiply



So %28%282x-6%29%2F21%29%2F%28%285x-15%29%2F12%29 simplifies to 8%2F35


In other words, %28%282x-6%29%2F21%29%2F%28%285x-15%29%2F12%29=8%2F35

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
(((2x-6)/21)/((5x-15)/12) multiply both the numerator and denominator by 12/(5x-15). This will make the denominator equal to 1 and thus get rid of the complex fraction.
((2x-6)/21)(12/(5x-15))/((5x-15)/12)(12/(5x-15)) and this equals
(12(2x-6))/(21(5x-15))/1 and this equals
24(x-3)/105(x-3)=24/105=8/35 check my work

Hope this helps---ptaylor

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x-6%29%2F21%29+%2F+%28%285x-15%29%2F12%29
%28%282x-6%29+%2F+21%29%2A%2812%2F%285x+-+15%29%29
divide top and bottom by 3
%28%282x-6%29+%2F+7%29%2A%284%2F%285x+-+15%29%29
%284%2F7%29%2A%28%282x-6%29+%2F+%285x+-+15%29%29
%284%2F7%29%2A%282%2F5%29%2A%28%28x-3%29+%2F+%28x-3%29%29
%284%2F7%29%2A%282%2F5%29
8%2F35 answer