Question

$\frac{x - 1}{x - 2} = \frac{2x - 1}{2x + 2}$
Будь ласка допоможіть!!!!​

Answer 1

Объяснение:

I see you've provided a mathematical equation in LaTeX format. To solve this equation for x, you can cross-multiply and then simplify:

\(\frac{x - 1}{x - 2} = \frac{2x - 1}{2x + 2}\)

Cross-multiply:

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

Expand both sides:

\(2x^2 + 2x - 2x - 2 = 2x^2 - 4x - x + 2\)

Simplify and combine like terms:

\(2x^2 = 2x^2 - 5x\)

Now, subtract \(2x^2\) from both sides:

\(0 = -5x\)

Finally, solve for x by dividing both sides by -5:

\(x = 0\)

So, the solution to the equation is \(x = 0\).

Answer 2

$\displaystyle\frac{x - 1}{x - 2} = \frac{2x - 1}{2x + 2}\\\\(2x+2)(x-1)=(2x-1)(x-2)\\2x^2+2x-2x-2 = 2x^2-x-4x+2\\-2=-5x+2\\5x=4\\x=0.8$