Question

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

Answer 1

Ответ:

фото__________________

Answer 2

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

Возведём к общему знаменателю:

$\frac{(x - 6)(x - 6)}{(x - 1)(x - 6)} + \frac{(x - 1)(x - 1)}{(x - 1)(x - 6)} = \frac{13}{6}$

Так как знаменатели равны, мы можем записать дроби под одним знаменателем:

$\frac{(x - 6)(x - 6) + (x - 1)(x - 1)}{(x - 1)(x + 6)} = \frac{13}{6}$

Запишем (х-6)(х-6) как (х-6)² и (х-1)(х-1) как (х-1)²:

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

$\frac{ {x}^{2} - 12x + 36 + {x}^{2} - 2x + 1}{(x - 1)(x - 6)} = \frac{13}{6}$

Приведём подобные слагаемые:

$\frac{2 {x}^{2} - 14x + 37 }{(x - 1)(x + 6)} = \frac{13}{6}$

$6(2 {x}^{2} - 14x + 37) = 13(x - 1)(x - 6) \\ \\ 12 {x}^{2} - 84x + 222 = (13x - 13)(x - 6) \\ \\ 12 {x}^{2} - 84x + 222 = 13 {x}^{2} - 78x - 13x + 78 \\ \\12 {x}^{2} - 84x + 222 = 13 {x}^{2} - 91x - 78$

$12 {x}^{2} - 84x + 222 - 13 {x}^{2} + 91x - 78 = 0 \\ \\ - {x}^{2} + 7x + 144 = 0$

Умножим уравнение на -1:

-х²+7х+144=0 |×(-1)

х²-7х-144=0

Решим за дискриминантом:

D=b²-4ac = 7²-4×1×(-144) = 49+576 = 625

$x1 = \frac{ - b + \sqrt{d} }{2a} = \frac{7 + 25}{2} = \frac{32}{2} = 16$

$x2 = \frac{ - b - \sqrt{d} }{2a} = \frac{7 - 25}{2} = \frac{ - 18}{2} = - 9$

Ответ: х=16 и х=(-9).

Answer 3

I can help you solve this equation step by step. Here is how I do it:

- First, I simplify the left side of the equation by finding the common denominator and adding the fractions. The common denominator is (x-1)(x-6), so I multiply the first fraction by (x-6)/(x-6) and the second fraction by (x-1)/(x-1). This gives me:

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

- Next, I expand the numerator and simplify it. I get:

[(x-6)(x-6) + (x-1)(x-1)]/[(x-1)(x-6)] = [(x^2 - 12x + 36) + (x^2 - 2x + 1)]/[(x-1)(x-6)] = (2x^2 - 14x + 37)/[(x-1)(x-6)]

- Then, I simplify the right side of the equation by converting the mixed number to an improper fraction. I get:

2 + 1/6 = (12 + 1)/6 = 13/6

- Now, I have a simpler equation to solve:

(2x^2 - 14x + 37)/[(x-1)(x-6)] = 13/6

- To solve this equation, I cross multiply and move everything to one side. I get:

(2x^2 - 14x + 37)(6) = (13)(x-1)(x-6)

12x^2 - 84x + 222 = 13x^2 - 91x + 78

-12x^2 + 7x - 144 = 0

- Finally, I use the quadratic formula to find the values of x that satisfy the equation. The quadratic formula is:

x = (-b ± √(b^2 - 4ac))/(2a)

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. In this case, a = -12, b = 7, and c = -144. Plugging these values into the formula, I get:

x = (-(7) ± √((7)^2 - 4(-12)(-144)))/(2(-12))

x = (-7 ± √(-6911))/(-24)

x = (-7 ± i√(6911))/(-24)

where i is the imaginary unit that satisfies i^2 = -1. These are the two complex solutions of the equation. There are no real solutions.

I hope this helps you understand how to solve this equation. If you want to check your answer or learn more about solving equations, you can use one of these online calculators . They will show you the steps and explanations for each problem.