If $ \frac{a}{a+b}=\frac{17}{23}, $ then find the value of $ \frac{a+b}{a-b} $
(write your answer in the simplest fractional form)
Given: $ \frac{a}{a+b}=\frac{17}{23}$
To Do: Find the value of $ \frac{a+b}{a-b} $
Solution:
$\frac{a}{a+ b}$= $\frac{17}{23}$
$23a = 17a + 17b$
$23a - 17a = 6a = 17b$
$\frac{a}{b} = \frac{17}{6}$
Then $\frac{a + b}{a - b} = \frac{17 + 6}{17 - 6}$
= $\frac{23}{11}$
So $\frac{a + b}{a - b} = \frac{23}{11}$
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