Question

(х-2) (х+2)\4=(х-1) (х+3)\3

Answer 1

Вот полное решение. Гарантирую, что всё правильно!

Answer 2

X1=-8,x2=0
мне кажется так.

Answer 3

To solve the equation $\frac{(x-2)(x+2)}{4} = \frac{(x-1)(x+3)}{3}$, we can start by cross-multiplying to eliminate the fractions.

Step 1: Cross-multiply

Multiply both sides of the equation by 4 and 3 to eliminate the fractions:

$4 \cdot \frac{(x-2)(x+2)}{4} = 4 \cdot \frac{(x-1)(x+3)}{3}$

$3 \cdot \frac{(x-2)(x+2)}{4} = 3 \cdot \frac{(x-1)(x+3)}{3}$

Step 2: Simplify

Cancel out common factors:

$x-2)(x+2) = \frac{4}{3}(x-1)(x+3)$

Step 3: Expand

Expand both sides of the equation:

$x^2 + 2x - 2x - 4 = \frac{4}{3}(x^2 + 3x - x - 3)$

Step 4: Further simplify

$x^2 - 4 = \frac{4}{3}(x^2 + 2x - 3)$

Step 5: Distribute

Distribute $\frac{4}{3}$ on the right-hand side:

$x^2 - 4 = \frac{4}{3}x^2 + \frac{8}{3}x - 4$

Step 6: Move all terms to one side

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

$x^2 - \frac{4}{3}x^2 - \frac{8}{3}x + 4 - 4 = 0$

Step 7: Combine like terms

Combine like terms:

$\frac{2}{3}x^2 - \frac{8}{3}x = 0$

Step 8: Factor out common terms

Factor out $x$ from the left side:

$\frac{2}{3}x(x - 4) = 0$

Step 9: Set each factor to zero

Now, we can set each factor to zero and solve for $x$:

1. $x = 0$

2. $x - 4 = 0$

Solving for $x$ in the second equation:

$x = 4$

So, the solutions to the equation are $x = 0$ and $x = 4$.