How do you solve #\frac { 5} { x } = \frac { 3} { x - 12}#?

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Answer 1 · 2017-07-16T17:21:36

#x = 30#

When you have an equation where the variable is on the denominator on both sides, cross-multiplication would be the way to go.

Multiplying both sides by #x(x-12)# (the common multiple)
#(5(x-12))/(x(x-12))=(3x)/(x(x-12))#

you can then cancel out the common denominator, leaving you with:
#5(x-12)=3x#

Distributing...
#5x-60=3x#

Subtracting #3x# from both sides
#2x - 60 = 0#

Adding 60 to both sides...
#2x = 60#

Finally dividing both sides by #2#...
#x = 60/2 = 30#

Therefore, #x = 30#