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)?
+592 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?
