Simplify the expression [g(x)-g(9)]/x-9

Jan 2016
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0
USA
Assume that g(x)=(x-2)/(x+2). Simplify the expression [g(x)-g(9)]/x-9.
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
$g(x) = \dfrac{x-2}{x+2}$

$\dfrac{g(x)-g(9)}{x-9} = \dfrac{\dfrac{x-2}{x+2} - \dfrac{7}{11}}{x-9}$

start by multiplying numerator & denominator by $11(x+2)$ to clear the fractions ...

$\dfrac{\dfrac{x-2}{x+2} - \dfrac{7}{11}}{x-9} \cdot \dfrac{11(x+2)}{11(x+2)} =\dfrac{11(x-2) - 7(x+2)}{11(x+2)(x-9)}$

simplify the numerator, factor the result, then you should see a cancellation.
 
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