Question

X+2/x-1+3/x+1=6/x 2 -4

Answer 1

х¹=1/2,х²=4

100 процентов правильно ,

Answer 2

1-2/(x-1)-6/(x-1)(x+1)-3/(x+1)=0
x≠1,x≠-1
x²-1-2x-2-6-3x+3=0
x²-5x-6=0
x1+x2=5 U x1*x2=-6
x1=-1 не удов усл
x2=6

Answer 3

To solve this equation:

(x + 2)/(x - 1) + 3/(x + 1) = 6/(x^2 - 4)

First, we should simplify the equation by factoring the denominator on the right side, which is the difference of squares:

x^2 - 4 = (x + 2)(x - 2)

Now, let's rewrite the equation with the factored denominator:

(x + 2)/(x - 1) + 3/(x + 1) = 6/((x + 2)(x - 2))

Next, we need to find a common denominator on the left side. The common denominator for (x - 1) and (x + 1) is (x^2 - 1), so let's rewrite the fractions with this common denominator:

[(x + 2)(x + 1)]/[(x - 1)(x + 1)] + [3(x - 1)]/[(x - 1)(x + 1)] = 6/((x + 2)(x - 2))

Now, the equation becomes:

[(x + 2)(x + 1) + 3(x - 1)]/[(x - 1)(x + 1)] = 6/((x + 2)(x - 2))

Now, we can cross-multiply to get rid of the fractions:

[(x + 2)(x + 1) + 3(x - 1)] * ((x + 2)(x - 2)) = 6 * [(x - 1)(x + 1)]

Expand both sides of the equation and simplify:

(x + 2)(x + 1)(x + 2)(x - 2) + 3(x - 1)(x + 2)(x - 2) = 6(x^2 - 1)

Now, let's continue simplifying:

(x^2 + 3x + 2)(x^2 - 4) + 3(x^2 - 4) = 6(x^2 - 1)

Now, distribute and simplify further:

x^4 - 2x^2 + 3x^3 - 12x + 2x^2 - 8 + 3x^2 - 12x = 6x^2 - 6

Now, combine like terms:

x^4 + 3x^3 - 12x^2 - 12x - 8 = 6x^2 - 6

Now, bring all terms to one side of the equation to set it to zero:

x^4 + 3x^3 - 12x^2 - 12x - 6x^2 + 8 - 6 = 0

Combine like terms again:

x^4 + 3x^3 - 18x^2 - 12x + 2 = 0

This is a quartic equation, and solving it for an exact solution is typically complex. You may need to use numerical methods or software to find approximate solutions.