Question

13 12 —— + —— =2 x-12 x-13

Answer 1

Ответ:

Нужно написать 20 символов, поэтому пишу этот ответ, а так все на фотке.

Answer 2

To solve the equation (13/x) + (12/(x-1)) = 2, we'll first find a common denominator and then solve for x:

Step 1: Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (x)(x-1):

(13/x) + (12/(x-1)) = 2

To get a common denominator, multiply the first fraction by (x-1)/(x-1) and the second fraction by (x/x):

[(13(x-1))/((x)(x-1))] + [(12x)/((x)(x-1))] = 2

Step 2: Combine the fractions on the left side of the equation:

[13(x-1) + 12x]/(x(x-1)) = 2

Step 3: Distribute and simplify the numerator on the left side:

[13x - 13 + 12x] / (x(x-1)) = 2

(25x - 13) / (x(x-1)) = 2

Step 4: Now, let's get rid of the fraction by multiplying both sides of the equation by (x)(x-1):

(x)(x-1) * [(25x - 13) / (x(x-1))] = 2 * (x)(x-1)

This will cancel out the denominators:

25x - 13 = 2x(x-1)

Step 5: Expand the right side of the equation:

25x - 13 = 2x^2 - 2x

Step 6: Move all terms to one side of the equation to set it equal to zero:

2x^2 - 2x - 25x + 13 = 0

Step 7: Combine like terms:

2x^2 - 27x + 13 = 0

Now, you have a quadratic equation. To solve for x, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2, b = -27, and c = 13. Plug these values into the quadratic formula:

x = (27 ± √((-27)² - 4(2)(13))) / (2(2))

x = (27 ± √(729 - 104)) / 4

x = (27 ± √625) / 4

x = (27 ± 25) / 4

Now, you have two possible solutions for x:

1. x = (27 + 25) / 4 = 52 / 4 = 13
2. x = (27 - 25) / 4 = 2 / 4 = 0.5

So, the equation has two solutions: x = 13 and x = 0.5.