Question

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

Answer 1

Ответ:

-3 2/3; 4 2/3

Объяснение:

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

((x-3)²+(x+2)²)/((x+2)(x-3))=17/4

4(x²-6x+9+x²+4x+4)=17(x²-x-6)

17x²-17x-102-8x²+8x-52=0

9x²-9x-154=0; D=81+5544=5625

x₁=(9-75)/18=-66/18=-11/3=-3 2/3

x₂=(9+75)/18=84/18=14/3=4 2/3

Answer 2

To solve the equation:

$\frac{{x-3}}{{x+2}} + \frac{{x+2}}{{x-3}} = \frac{{4}}{{4}}$

We can start by simplifying the left side of the equation by finding a common denominator:

$\frac{{(x-3)^2}}{{(x+2)(x-3)}} + \frac{{(x+2)^2}}{{(x+2)(x-3)}} = \frac{{4}}{{4}}$

Expanding the squares in the numerators:

$\frac{{x^2 - 6x + 9}}{{x^2 - x - 6}} + \frac{{x^2 + 4x + 4}}{{x^2 - x - 6}} = \frac{{4}}{{4}}$

Combining the fractions:

$\frac{{x^2 - 6x + 9 + x^2 + 4x + 4}}{{x^2 - x - 6}} = \frac{{4}}{{4}}$

Simplifying the numerator:

$\frac{{2x^2 - 2x + 13}}{{x^2 - x - 6}} = 1$

Now, we can cross-multiply:

$2x^2 - 2x + 13 = x^2 - x - 6$

Bringing all terms to one side:

$2x^2 - x^2 - 2x + x + 13 + 6 = 0$

$x^2 - x + 19 = 0$

Unfortunately, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

$x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(19)}}}}{{2(1)}}$

Simplifying:

$x = \frac{{1 \pm \sqrt{{1 - 76}}}}{{2}}$

$x = \frac{{1 \pm \sqrt{{-75}}}}{{2}}$

Since the discriminant is negative, the equation has no real solutions. The given equation does not have a valid solution in the real number system.