To solve the equation, first find a common denominator for all the fractions on the left side of the equation:
a/a^2-16 = a/(a^2-16) = a/((a+4)(a-4))
2/a-4 = 2/(a-4)
So the equation becomes: a/(a^2-16) + 2/(a-4) = 2/(a+4)
Now multiply each fraction by the LCD (a+4)(a-4):
a(a+4) + 2(a+4) = 2(a-4)
Expand and simplify:
a^2 + 4a + 2a + 8 = 2a - 8
a^2 + 6a + 8 = 2a - 8
a^2 + 6a - 2a = -8 - 8
a^2 + 4a = -16
a(a+4) = -16
Now you have:
a(a+4) = -16
This equation has two solutions: a = -16 or a = 4.
So the solutions are a) -16 and b) 4.
To check the solution, you can substitute each value back into the original equation and see if it satisfies the equation.
solve the equation. check the solution.
a/a^2-16 + 2/a-4 = 2/a+4
a) -16,-4
b) 4
c) -16,4
d) -16
1 answer
1 answer