Question

(40/3)/(х+4)+(28/3)/(х-4)=1

Answer 1

Фото во вложении)))))

Answer 2

To solve the equation:

(40/3)/(x+4) + (28/3)/(x-4) = 1

We can simplify it by finding a common denominator. The common denominator for (x+4) and (x-4) is (3)(x+4)(x-4).

Multiplying every term by (3)(x+4)(x-4), we get:

[(40/3)/(x+4)] * (3)(x+4)(x-4) + [(28/3)/(x-4)] * (3)(x+4)(x-4) = 1 * (3)(x+4)(x-4)

Simplifying:

40(x-4) + 28(x+4) = 3(x+4)(x-4)

Now, expand the terms:

40x - 160 + 28x + 112 = 3(x^2 - 16)

Combine like terms:

68x - 48 = 3x^2 - 48

Rearrange the equation to form a quadratic equation:

3x^2 - 68x + 48 = 0

Now, we can solve this quadratic equation. Factoring might not work here, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -68, and c = 48. Plugging in these values:

x = (-(-68) ± √((-68)^2 - 4(3)(48))) / (2(3))

Simplifying further:

x = (68 ± √(4624 - 576)) / 6

x = (68 ± √4048) / 6

x = (68 ± 63.66) / 6

Now we solve for the two possible values of x:

x1 = (68 + 63.66) / 6 = 131.66 / 6 ≈ 21.94

x2 = (68 - 63.66) / 6 = 4.34 / 6 ≈ 0.72

Therefore, the equation has two solutions: x ≈ 21.94 and x ≈ 0.72.