5/х-1+30/х+1=5

To solve the equation (5/x-1) + (30/x+1) = 5, we can start by finding a common denominator for the fractions. In this case, the common denominator is (x - 1)(x + 1).

So, let's rewrite the equation with the common denominator:

(5(x + 1) + 30(x - 1)) / (x - 1)(x + 1) = 5

Expanding and simplifying the equation, we have:

(5x + 5 + 30x - 30) / (x - 1)(x + 1) = 5

(35x - 25) / (x - 1)(x + 1) = 5

Now, let's multiply both sides of the equation by the common denominator:

(35x - 25) = 5(x - 1)(x + 1)

Let's distribute on the right side of the equation:

35x - 25 = 5(x^2 - 1)

Expand further:

35x - 25 = 5x^2 - 5

Now, let's bring all terms to one side of the equation:

5x^2 - 35x + 5 - 25 = 0

5x^2 - 35x - 20 = 0

Divide the equation by 5 to simplify:

x^2 - 7x - 4 = 0

The equation is now in standard form. To solve it, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

For this equation, a = 1, b = -7, and c = -4.

x = (-(-7) ± √((-7)^2 - 4(1)(-4))) / (2(1))

x = (7 ± √(49 + 16)) / 2

x = (7 ± √65) / 2

Therefore, the solutions to the equation are x = (7 + √65) / 2 and x = (7 - √65) / 2.