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The problem

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I was taught that to remove a fraction multiply both side by a factor of the numerator. In the problem the x-3 was multiply by 5 but the fraction was not why is that.

Answer provided by our tutors

You probably meant denominator not numerator. The fraction is also multiplied by it, but it gets cancelled with the fraction's denominator, which is also equal to 5 -- so neither "5" shows because they cancel each other:

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