(-x^2-2x+15)/(x^2-4x)=0

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вопрос

To solve the equation ((-x^2-2x+15)/(x^2-4x) = 0), we first need to find the values of (x) that make the expression on the left side equal to zero.

Setting the numerator (-x^2-2x+15) equal to zero, we have:
[-x^2-2x+15 = 0]

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring:
[-x^2-2x+15 = -(x^2+2x-15) = -(x-3)(x+5) = 0]

This gives us two possible solutions: (x = 3) and (x = -5).

Next, we need to find the values of (x) that make the denominator (x^2-4x) equal to zero to avoid division by zero.

Setting the denominator equal to zero, we have:
[x^2-4x = 0]
[x(x-4) = 0]

This gives us two additional possible solutions: (x = 0) and (x = 4).

So, combining the solutions from the numerator and denominator, the values of (x) that satisfy the equation ((-x^2-2x+15)/(x^2-4x) = 0) are (x = -5), (x = 0), (x = 3), and (x = 4).