Question

Виведіть х t^3 = (x+1) \ (x-1)

Answer 1

$t^3=\frac{x+1}{x-1}$

Умножаем обе части на $(x-1)$

$t^3(x-1)=x+1\\t^3x-t^3=x+1$

Перенесем все икс в одну сторону, остальное в другую

$t^3x-x=t^3+1\\x(t^3-1)=t^3+1\\x=\frac{t^3+1}{t^3-1}$

Answer 2

To solve the equation $xt^3 = \frac{x+1}{x-1}$, we'll first try to isolate $x$ on one side of the equation. Here's how you can do it step by step:

Step 1: Multiply both sides by $x-1$ to get rid of the fraction on the right-hand side:

$x(t^3)(x-1) = x+1.$

Step 2: Expand the left-hand side:

$x(t^3)(x-1) = xt^3 \cdot x - xt^3 = x^2t^3 - xt^3.$

Step 3: Now, subtract $x+1$ from both sides:

$x^2t^3 - xt^3 = x+1 - x.$

Step 4: Simplify the equation:

$x^2t^3 - xt^3 = 1.$

Step 5: Factor out $x^2t^3$ on the left-hand side:

$x^2t^3(1 - t) = 1.$

Step 6: Finally, solve for $x$:

$x = \frac{1}{t^3(1 - t)}.$

So, the solution for $x$ in terms of $t$ is $x = \frac{1}{t^3(1 - t)}$.