Question

(x^(2)+2x-3)/(x^2-4x+3)=0

Answer 1

Ответ:

Дробь равна 0, когда числитель равен 0

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По теореме Виета:

x₁+x₂=4

x₁*x₂=3

x₁≠3

x₂≠4

Ответ:-3,1

Answer 2

To solve the equation $\frac{{x^2 + 2x - 3}}{{x^2 - 4x + 3}} = 0$, we can start by factoring the numerator and the denominator, and then find the values of $x$ that make the fraction equal to zero.

First, let's factor the numerator and denominator separately:

Numerator: $x^2 + 2x - 3 = (x - 1)(x + 3)$

Denominator: $x^2 - 4x + 3 = (x - 1)(x - 3)$

Now we can rewrite the equation as:

$\frac{{(x - 1)(x + 3)}}{{(x - 1)(x - 3)}} = 0$

Notice that we have a common factor of $(x - 1)$ in both the numerator and the denominator. We can cancel out this common factor:

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

Now we have a fraction equal to zero. For a fraction to be zero, the numerator must be zero. Therefore, we set $x + 3 = 0$ and solve for $x$:

$x + 3 = 0$

Subtracting 3 from both sides:

$x = -3$

So the solution to the equation is $x = -3$.