Question

(x ^ 2 + 1)/(x + 1) = 1​

Answer 1

Ответ: х=1

Объяснение:

(x ^ 2 + 1)/(x + 1) = 1​             (пропорция)

x^2+1=x+1

x^2=x             (делим на х)

x=1

Answer 2

To solve the equation $\frac{{x^2 + 1}}{{x + 1}} = 1$, we'll begin by multiplying both sides of the equation by $x + 1$ to eliminate the denominator:

$\frac{{x^2 + 1}}{{x + 1}} \cdot (x + 1) = 1 \cdot (x + 1)$

Simplifying the equation:

$x^2 + 1 = x + 1$

Next, let's move all terms to one side of the equation:

$x^2 - x = 0$

Now, we have a quadratic equation. To solve it, we factor out $x$:

$x(x - 1) = 0$

Now, we can set each factor equal to zero:

$x = 0$ or $x - 1 = 0$

Solving for $x$ in each case:

For $x = 0$, we substitute it back into the original equation to verify if it's a valid solution:

$\frac{{0^2 + 1}}{{0 + 1}} = 1$

$\frac{1}{1} = 1$

The equation holds true for $x = 0$.

For $x - 1 = 0$, we solve for $x$:

$x = 1$

Similarly, we substitute $x = 1$ back into the original equation:

$\frac{{1^2 + 1}}{{1 + 1}} = 1$

$\frac{2}{2} = 1$

Again, the equation holds true for $x = 1$.

Therefore, the solutions to the equation $\frac{{x^2 + 1}}{{x + 1}} = 1$ are $x = 0$ and $x = 1$.