Question 666968
Establish variables
x = numerator
y = denominator
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Given
y = x+5
{{{(x-2)/(y-2) = 7/12}}}
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Substitute y into the second equation
{{{(x-2)/((x+5)-2) = 7/12}}}

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Cross multiply
12(x-2) = 7((x+5)-2)
12x - 24 = 7x + 35 - 14
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Combine like terms
12x - 7x = 35 - 14 + 24
5x = 45
x = 9
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y = x+5 = 9+5 = 14
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{{{highlight_green(9/14)}}}
Which was the long way of seeing that 
{{{(7+2)/(12+2) = 9/14}}}
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