Question

(х^2+х-5)/х +3х/(х^2+х-5) +4=0

Answer 1

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Answer 2

To solve the given equation, we'll first simplify it and then solve for the variable.

The equation is:

(х^2 + х - 5) / х + 3х / (х^2 + х - 5) + 4 = 0

Let's simplify the expression by finding a common denominator:

[(х^2 + х - 5) + 3х] / (х^2 + х - 5) + 4 = 0

[(х^2 + 4х - 5) / (х^2 + х - 5)] + 4 = 0

Now, let's combine the terms over the common denominator:

(х^2 + 4х - 5 + 4(х^2 + х - 5)) / (х^2 + х - 5) = 0

(х^2 + 4х - 5 + 4х^2 + 4х - 20) / (х^2 + х - 5) = 0

(5х^2 + 8х - 25) / (х^2 + х - 5) = 0

Now, let's factorize the quadratic expressions in the numerator and denominator:

5х^2 + 8х - 25 = 0

(5х - 5)(х + 5) = 0

х = 5/5 or х = -5

Now, let's consider the denominator (х^2 + х - 5) and set it equal to zero:

х^2 + х - 5 = 0

Using the quadratic formula:

х = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = 1, and c = -5.

х = (-1 ± √(1^2 - 4(1)(-5))) / (2(1))

х = (-1 ± √(1 + 20)) / 2

х = (-1 ± √21) / 2

Therefore, the solutions to the equation are:

х = 5/5, х = -5, and х ≈ (-1 ± √21) / 2.