Question

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

Answer 1

28 у меня так вишло

Answer 2

To solve the equation 3*(3x-1)/(3x-2) = 2 + (3x+1)/(3x-1), we'll start by simplifying both sides of the equation and then finding the value of x.

Step 1: Simplify the left-hand side of the equation: 3*(3x-1)/(3x-2)

To simplify the expression, first distribute the 3: 3 * 3x = 9x 3 * (-1) = -3

So the expression becomes: (9x - 3)/(3x - 2)

Step 2: Simplify the right-hand side of the equation: 2 + (3x + 1)/(3x - 1)

Step 3: Find a common denominator for the fractions on the right-hand side: The common denominator is (3x - 1).

So, rewrite 2 as (2 * (3x - 1))/(3x - 1): (2 * (3x - 1))/(3x - 1) + (3x + 1)/(3x - 1)

Step 4: Combine the fractions on the right-hand side: [(2 * (3x - 1) + (3x + 1))/(3x - 1)]

Step 5: Distribute and combine the terms: [(6x - 2 + 3x + 1)/(3x - 1)]

Now, combine like terms: [(9x - 1)/(3x - 1)]

Now that we have both sides of the equation simplified, we can set them equal to each other:

(9x - 3)/(3x - 2) = (9x - 1)/(3x - 1)

To solve for x, we'll eliminate the denominators. Cross-multiply:

(9x - 3)(3x - 1) = (9x - 1)(3x - 2)

Now, expand both sides:

27x^2 - 9x - 3x + 1 = 27x^2 - 18x - 9x + 2

Combine like terms:

27x^2 - 12x + 1 = 27x^2 - 27x + 2

At this point, the x^2 terms will cancel out when we move all terms to one side:

27x^2 - 27x + 2 - (27x^2 - 12x + 1) = 0

27x^2 - 27x + 2 - 27x^2 + 12x - 1 = 0

Simplify:

-15x + 1 = 0

Now, isolate x:

-15x = -1

x = -1 / -15

x = 1/15

So the solution to the equation is x = 1/15.