Х+4/ х-5+х / х+5= 50 / х^2- 25

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To start, let's simplify the left side of the equation:

(Х + 4) / (Х - 5) + Х / (Х + 5)

To add these fractions with different denominators, we need to find a common denominator:

= [(Х + 4)(Х + 5) + Х(Х - 5)] / (Х - 5)(Х + 5)
= (Х^2 + 5Х + 4Х + 20 + Х^2 - 5Х) / (Х^2 - 25)
= (2Х^2 + 4Х + 20) / (Х^2 - 25)
= 2(Х^2 + 2Х + 10) / (Х + 5)(Х - 5)

Now our equation looks like this:

2(Х^2 + 2Х + 10) / (Х + 5)(Х - 5) = 50 / (Х^2 - 25)

To solve for Х, we can multiply both sides by (Х + 5)(Х - 5) to get rid of the denominators:

2(Х^2 + 2Х + 10) = 50(Х^2 - 25)

Now let's expand and simplify:

2Х^2 + 4Х + 20 = 50Х^2 - 1250
48Х^2 - 2Х^2 - 4Х - 1250 - 20 = 0
46Х^2 - 4Х - 1270 = 0

This is a quadratic equation that can be solved using the quadratic formula:

Х = [-(-4) ± √((-4)^2 - 446(-1270))] / 2*46
Х = [4 ± √(16 + 233840)] / 92
Х = [4 ± √233856] / 92
Х = [4 ± 484] / 92

Therefore, the solutions for Х are:

Х = (4 + 484) / 92 => Х = 488 / 92 => Х = 122 / 23
and
Х = (4 - 484) / 92 => Х = -480 / 92 => Х = -240 / 46 => Х = -120 / 23

So, the solutions are Х = 122 / 23 or Х = -120 / 23.