To solve the equation, first find a common denominator for the fractions on the left side of the equation. The common denominator is x^2 - 25 = (x - 5)(x + 5).
(1/(x-5) + 1/(x+5)) = (x+5 + x-5) / ((x-5)(x+5))
= 2x / (x^2 - 25)
Thus the equation becomes:
2x / (x^2 - 25) = 10 / (x^2 - 25)
Then cross multiply:
2x(x^2 - 25) = 10(x^2 - 25)
2x^3 - 50x = 10x^2 - 250
Move all terms to one side of the equation:
2x^3 - 10x^2 - 50x + 250 = 0
Now factor out a 2 from all terms:
2(x^3 - 5x^2 - 25x + 125) = 0
This equation doesn't have any easy integer or simplified fraction solutions, so the final answer is:
B) there are infinitely many solutions
solve the following equation. check the solution
1/x-5+1/x+5=10/x^2-25
select the correct choice below and if necessary fill in the answer box to complete your choice
A the solution is (type an integer or simplified fraction use a comma to separate answers as needed
B there are infinitely many solutions
C there is no solution
1 answer