Question

2/2х-1+3/х-3=1+х/х-3+х/2х-1

Answer 1

2(2х-1)-3(х-2)=6+4(3-2х)

4x-2-3x+6=6+12-8x

4x-3x+8x=6+12+2-6

9x=14

x=1 целая пять девятых

Answer 2

To solve the equation 2/(2x - 1) + 3/(x - 3) = 1 + x/(x - 3) + x/(2x - 1), we can start by simplifying the expression on both sides of the equation and then solving for x.

First, let's find the common denominator for all the fractions involved, which is (2x - 1)(x - 3)(2x - 1)(x - 3). Multiply each term by the appropriate factors to get rid of the denominators:

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

Now, distribute and simplify:

2(2x^2 - 7x + 3) + 3(2x - 1) = 2x^2 - 7x + 3 - 3x + 9 + 2x^2 - x

4x^2 - 14x + 6 + 6x - 3 = 4x^2 - 7x + 3

Now, combine like terms:

4x^2 - 14x + 6x - 7x - 3 + 3 = 4x^2 - 7x + 3

4x^2 - 15x = 4x^2 - 7x + 3

Next, subtract 4x^2 - 7x + 3 from both sides to get:

4x^2 - 15x - (4x^2 - 7x + 3) = 0

4x^2 - 15x - 4x^2 + 7x - 3 = 0

Simplify and combine like terms:

-8x + 4 = 0

Now, isolate the variable by moving the constant term to the other side:

-8x = -4

Divide both sides by -8 to solve for x:

x = (-4)/(-8)

Simplify the right side:

x = 1/2

Therefore, the solution to the equation is x = 1/2.