math destroyer question

[spoog74]

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question goes like this;

[1/5-1/x] / [5/x-1] is equivalent to ?


Answer is -1/5


The explanation says you multiply the whole expression by one in the form of 5x/5x so we get [x-5]/ [25-5x] <---- How did they get 25-5x in the denominator? Ive been trying to work it out but cant get it...

 

[carlfusco]

5x[(5/x)-1] = 5x*(5/x) - 5x*1 ----> 25-5x

Think of it in parts... 5x * 5/x = 25x/x (x's cancel), 5x*1=5x... see it now?

 

[ekephant]

(1/5 - 1/x)5x / (5/x - 1)5x = (5x/5 - 5x/x) / (25x/x - 5x)

cancel out the like terms and you get: (x-5) / (25-5x)
then factor out to get: -1(-x+5) / 5(5-x), rewritten as -1(5-x) / 5(5-x)
cancel the like term and you get -1/5