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Solve the equation. Show all work.
a/a^2-25 + 2/a+5 = 2/a-5
Bot GPT 3.5
answered
To solve this equation, we need to find a common denominator and then combine the fractions.
Given equation: a/(a^2 - 25) + 2/(a + 5) = 2/(a - 5)
The common denominator is (a - 5)(a + 5) = a^2 - 25.
Rewrite the equation with the common denominator:
a/(a^2 - 25) + 2/(a + 5) = 2/(a - 5)
a/(a^2 - 25) + 2(a - 5)/(a - 5)(a + 5) = 2/(a - 5)
Now combine the fractions:
a/(a^2 - 25) + 2(a - 5)/(a^2 - 25) = 2/(a - 5)
a + 2(a - 5) = 2
Expand and simplify:
a + 2a - 10 = 2
3a - 10 = 2
3a = 12
a = 4
Therefore, the solution to the equation is a = 4.