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Find all real numbers a that satisfy
1/(a^3 + 7) - 7 = -a^3/(a^3 + 7) + 5.

 Oct 11, 2022
 #1
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Notice how a long of the terms share a denominator of a^3 + 7, so we can multiply every term in the equation by a^3 + 7.

1 - 7(a^3 + 7) = -a^3 + 5(a^3 + 7)

a^3 + 1 = 12(a^3 + 7)

a^3 + 1 = 12a^3 + 84

11a^3 = -83

a = cube root of -83/11

 Oct 11, 2022

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