To solve this equation, we first need to find a common denominator for all three fractions:
(x-2)(x+5) for the left side of the equation, an(x-2)(x+5) for the right side of the equation.
After finding the common denominator, the equation becomes:
(x(x+5) - 8(x-2)) / (x-2)(x+5) = 14 / (x+5)(x-2)
Expanding and simplifying the numerators of the fractions on the left side, the equation becomes:
(x^2 + 5x - 8x + 16) / (x-2)(x+5) = 14 / (x+5)(x-2)
(x^2 - 3x + 16) / (x-2)(x+5) = 14 / (x+5)(x-2)
Now we can simplify the equation by clearing the denominators:
(x^2 - 3x + 16) = 14
Rearranging the equation gives:
x^2 - 3x + 16 - 14 = 0
x^2 - 3x + 2 = 0
Now, we factor the quadratic equation:
(x-2)(x-1) = 0
This gives us two possible solutions:
x = 2 or x = 1
Therefore, the solutions to the equation are x = 2 and x = 1.
To solve this equation, we first need to find a common denominator for all three fractions:
(x-2)(x+5) for the left side of the equation, an
(x-2)(x+5) for the right side of the equation.
After finding the common denominator, the equation becomes:
(x(x+5) - 8(x-2)) / (x-2)(x+5) = 14 / (x+5)(x-2)
Expanding and simplifying the numerators of the fractions on the left side, the equation becomes:
(x^2 + 5x - 8x + 16) / (x-2)(x+5) = 14 / (x+5)(x-2)
(x^2 - 3x + 16) / (x-2)(x+5) = 14 / (x+5)(x-2)
Now we can simplify the equation by clearing the denominators:
(x^2 - 3x + 16) = 14
Rearranging the equation gives:
x^2 - 3x + 16 - 14 = 0
x^2 - 3x + 2 = 0
Now, we factor the quadratic equation:
(x-2)(x-1) = 0
This gives us two possible solutions:
x = 2 or x = 1
Therefore, the solutions to the equation are x = 2 and x = 1.