Question

X+1/x-3+12/x+3=24/x2-9

Answer 1

$\frac{x+1}{x-3}+\frac{12}{x+3}=\frac{24}{x^{2} -9}\\\\\frac{x^{2}+3x+x+3+12x-36 }{(x-3)(x+3)}=\frac{24}{x^{2}-9 }\\\\\frac{x^{2}+16x-33 }{x^{2}-9 }=\frac{24}{x^{2}-9 } \\\\\left \{ {{x^{2}+16x-33=24 } \atop {x\neq-3;x\neq 3 }} \right.\\\\x^{2} +16x-57=0\\\\D=16^{2}-4*(-57)=256+228=484=22^{2}\\\\x_{1}=\frac{-16+22}{2}=3\\\\x_{2}=\frac{-16-22}{2}=-\frac{38}{2}=-19$

Ответ : - 19

Answer 2

To solve this equation, we need to first get rid of the denominators by finding a common denominator. In this case, the common denominator is (x-3)(x+3)(x), so we need to multiply both sides of the equation by this common denominator:

(x-3)(x+3)(x) * (X+1)/(x-3) + (x-3)(x+3)(x) * 12/(x+3) = (x-3)(x+3)(x) * 24/(x^2-9)

Simplifying the left-hand side by canceling out the common factors, we get:

(x+1)(x+3) + 12(x-3) = 24

Expanding and simplifying:

x^2 + 4x - 9 + 12x - 36 = 24

x^2 + 16x - 69 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 16, and c = -69. Plugging these values into the formula, we get:

x = (-16 ± sqrt(16^2 - 4(1)(-69))) / 2(1)

x = (-16 ± sqrt(400)) / 2

x = (-16 ± 20) / 2

x = -8 or x = 5.5

Therefore, the solutions to the equation are x = -8 and x = 5.5.