Question

(X+2/x-2)+(x-2/x+2)=13 Хелпб

Answer 1

$\frac{x+2}{x-2}+\frac{x-2}{x+2} =13$   |* (x-2)(x+2)

ОДЗ: х≠±2

$(x+2)^2+(x-2)^2 =13(x^2-4)$

$x^2+4x+4+x^2-4x+4=13x^2-52$

$2x^2+8=13x^2-52$

$52+8=13x^2-2x^2$

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$x_1=\sqrt{\frac{60}{11} } =\frac{2\sqrt{15} }{\sqrt{11} } \\ x_2=-\sqrt{\frac{60}{11} } =-\frac{2\sqrt{15} }{\sqrt{11} }$

Answer 2

Sure, I can help you solve the equation. Let's first simplify the left-hand side of the equation by finding a common denominator for the two fractions:

Step 1: Find a common denominator for (x+2)/(x-2) and (x-2)/(x+2): The common denominator is (x-2)(x+2).

Step 2: Rewrite the fractions with the common denominator: [(x+2)(x+2)/(x-2)(x+2)] + [(x-2)(x-2)/(x+2)(x-2)]

Step 3: Combine the fractions: [(x^2 + 4x + 4) + (x^2 - 4x + 4)] / [(x-2)(x+2)]

Step 4: Simplify the numerator: (2x^2 + 8) / [(x-2)(x+2)]

Now, the equation becomes: (2x^2 + 8) / [(x-2)(x+2)] = 13

Step 5: Cross-multiply to get rid of the denominator: 2x^2 + 8 = 13(x-2)(x+2)

Step 6: Expand the right-hand side: 2x^2 + 8 = 13(x^2 - 4)

Step 7: Distribute 13 on the right side: 2x^2 + 8 = 13x^2 - 52

Step 8: Move all terms to one side to set the equation to zero: 13x^2 - 2x^2 = 8 + 52

Step 9: Combine like terms: 11x^2 = 60

Step 10: Divide by 11 to isolate x^2: x^2 = 60/11

Step 11: Take the square root of both sides to solve for x: x = ±√(60/11)

Step 12: Simplify the square root: x = ±√(60)/√(11) x = ±(2√15)/√11 x ≈ ±(2.5247)/3.3166

Therefore, the two solutions for x are approximately: x ≈ 0.7612 or x ≈ -0.7612