Solve.

start fraction 8 over x end fraction plus start fraction 15 over x squared end fraction equals negative 1

1 answer

To solve the equation, we first need to combine the two fractions on the left side:

8/x + 15/x^2 = -1

We need to find a common denominator for the fractions, which in this case is x^2. We then rewrite the fractions:

(8x/x^2) + (15/x^2) = -1

Simplify the fractions:

8x/x^2 + 15/x^2 = -1
8x + 15 = -x^2

Rearrange the equation to make it equal to 0:

x^2 + 8x + 15 = 0

Now we need to factor the quadratic equation:

(x + 5)(x + 3) = 0

Set each factor to zero:

x + 5 = 0 or x + 3 = 0

Solve for x:

x = -5 or x = -3

Therefore, the solutions to the equation are x = -5 or x = -3.