SOLUTION: Please show me how to solve this with detailed workings (ie: how to cross multiply), thank you! 13/(3x-9)=2/(6-x)

Question 1021448: Please show me how to solve this with detailed workings (ie: how to cross multiply), thank you!
13/(3x-9)=2/(6-x)
Found 2 solutions by Boreal, Alan3354:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
13/(3x-9)=2/(6-x)
13/3(x-3)=2/(6-x)
13*(6-x) is top left times bottom right. It is 78-13x
3(x-3)*2, or (3x-9)*2)=6x-18 bottom left times top right
6x-18=78-13x
19x=96
x=(96/19)
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13/(288/19)-171/19)=2/(114-19)-96/19, to use common denominator of 19
13/(117/19)=2/(18/19)
divide by a fraction, invert and multiply
13*19/117 should equal 38/18
247/117 should equal 19/9
divide top and bottom of 247/117 and get 19/9, checks

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If a/b = c/d
Cross multiply --> ad = bc
---
It's a shortcut method of multiplying thru by the common denominator bd.
a/b = c/d
(a/b)*bd = (c/d)*bd
ad = bc
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