What is the value of<br>\frac{a^{2}+ac}{a^{2}c-c^{3}}-\frac{a^{2}-c^{2}}{a^{2}c+2ac^{2}+c^{3}}-\frac{2c}{a^{2}-c^{2}}+\frac{3}{a+c}?

Explanation

Simplifying the terms: the first is \frac{a(a+c)}{c(a-c)(a+c)} = \frac{a}{c(a-c)}, the second is \frac{(a-c)(a+c)}{c(a+c)^2} = \frac{a-c}{c(a+c)}. Their difference is \frac{3ac-c^2}{c(a^2-c^2)} = \frac{3a-c}{a^2-c^2}. Subtracting the third term \frac{2c}{a^2-c^2} gives \frac{3(a-c)}{(a-c)(a+c)} = \frac{3}{a+c}. Adding the fourth term yields \frac{6}{a+c}.

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