Question

21/x+1-16/x-2 +6/x=0

Answer 1

Ответ:

Вроде так)

Пошаговое объяснение:

Answer 2

To solve the equation $\frac{21}{x+1} - \frac{16}{x-2} + \frac{6}{x} = 0$, we need to find the values of $x$ that satisfy the equation.

To simplify the equation, let's find a common denominator for all the terms on the left-hand side. The common denominator is $x(x+1)(x-2)$.

Now, let's rewrite the equation with the common denominator:

$\frac{21(x(x-2))}{x(x+1)(x-2)} - \frac{16(x+1)(x)}{x(x+1)(x-2)} + \frac{6(x+1)(x-2)}{x(x+1)(x-2)} = 0$

Now, combine the fractions:

$\frac{21x(x-2) - 16(x+1)(x) + 6(x+1)(x-2)}{x(x+1)(x-2)} = 0$

Next, let's simplify the numerator:

$21x(x-2) - 16(x+1)(x) + 6(x+1)(x-2)$ $= 21x^2 - 42x - 16x^2 - 16x + 6x^2 - 6$ $= (21 - 16 + 6)x^2 + (-42 - 16)x - 6$ $= 11x^2 - 58x - 6$

So, the equation becomes:

$\frac{11x^2 - 58x - 6}{x(x+1)(x-2)} = 0$

To solve for $x$, we set the numerator equal to zero:

$11x^2 - 58x - 6 = 0$

Now, we can use the quadratic formula to find the values of $x$:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a = 11$, $b = -58$, and $c = -6$.

$x = \frac{-(-58) \pm \sqrt{(-58)^2 - 4 \cdot 11 \cdot (-6)}}{2 \cdot 11}$

$x = \frac{58 \pm \sqrt{3364 + 264}}{22}$

$x = \frac{58 \pm \sqrt{3628}}{22}$

$x = \frac{58 \pm 60.238}{22}$

Now, we have two potential solutions:

$x_1 = \frac{58 + 60.238}{22} \approx 5.736$

$x_2 = \frac{58 - 60.238}{22} \approx -0.106$

So, the solutions to the equation are approximately $x \approx 5.736$ and $x \approx -0.106$.