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# system

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If a and b satisfy

2a/(a - 2b) - 6b/(a + 2b) = 3

a/(a - 2b) + 6b/(a + 2b) = -1

What is ab/(a^2 - 4b^2)?

Mar 7, 2021

#1
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Start by simplifying the terms:

$$\frac{2a}{a-2b} - \frac{6b}{a+2b} = 3$$

$$\frac{(2a)(a+2b)-(6b)(a-2b)}{(a-2b)(a+2b)} = 3$$

$$\frac{2a^2 -2ab +12b^2}{(a-2b)(a+2b)} = 3$$

$$\frac{2a^2 -2ab +12b^2}{a^2-4b^2} = 3$$

$$\frac{a}{a-2b}+\frac{6b}{a+2b}=-1$$

$$\frac{(a)(a+2b)+(6b)(a-2b)}{(a-2b)(a+2b)}=-1$$

$$\frac{a^2+8ab-12b^2}{(a-2b)(a+2b)}=-1$$

$$\frac{a^2+8ab-12b^2}{a^2-4b^2}=-1$$

Can you take it from there?

Mar 7, 2021