Assuming this problem is a simplification problem, the best way to simplify a problem like this would be to combine the fractions. to combine fractions with different denominators, even with variables, would be to multiply and get equal denominators, and then simplify. To get equal fractions we simply multiply the 2nd denominator on both sides in the 1st and vice versa. In this case for the top we have 1/(z-4) and 2/(z+8), so then we multiply the denominators and get (z+8)/(z-4)(z+8) and 2(z-4)/(z-4)(z+8). To get the final numerator then we first multiply out the 2 and get 2z-8 on the right, then combine the two fractions by adding them, and get 3z/(z-4)(z+8). For the denominator we repeat the same process. We multiply the denominators to get 4(z-6)/(z+8)(z-6) and 3(z+8)/(z-6)(z+8) we simplify the numerators by multiplying the 4 and 3 to get 4z-24 and 3z+24, and then subtract. We then get 4z-24-3z-24 and so z-48 and (z-48)/(z-6)(z+8). So now we have 3z/(z-4)(z+8) for a numerator and (z-48)/(z-6)(z+8) as a denominator. we can multiply z-8 on both sides of the final fraction to cancel out the z-8, and so get 3z/(z-4)/(z-48)/(z-6). As you can no longer simplify anything this is your final fraction.

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4 years ago