Question

1.а)3х-х²/2 + 2х²-х/6=хб)х²/2-х=3х/2-хв)х-7/х-2 + х+4/x+2=1дам 40 баллов​

Answer 1

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Answer 2

Let's solve each equation step by step:

а) $3x - \frac{x^2}{2} + 2x^2 - \frac{x}{6} = x$

To solve this equation, let's first combine the like terms:

$3x + 2x^2 - \frac{x^2}{2} - \frac{x}{6} = x$

Next, let's get rid of the fractions by multiplying all terms by 6:

$6(3x) + 6(2x^2) - 6\left(\frac{x^2}{2}\right) - 6\left(\frac{x}{6}\right) = 6x$

Simplifying:

$18x + 12x^2 - 3x^2 - x = 6x$

Now, combine like terms again:

$18x + 9x^2 - x = 6x$

Move all terms to one side of the equation:

$18x + 9x^2 - x - 6x = 0$

$9x^2 + 11x = 0$

Now, factor out the common term:

$x(9x + 11) = 0$

Now, set each factor equal to zero and solve for x:

$x = 0$ or $9x + 11 = 0$

If $9x + 11 = 0$, then $9x = -11$, and $x = \frac{-11}{9}$.

So the solutions to the equation are $x = 0$ or $x = \frac{-11}{9}$.

б) $\frac{x^2}{2} - x = \frac{3x}{2} - x$

Let's first combine like terms:

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

Simplify:

$\frac{x^2}{2} - x = \frac{x}{2}$

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

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

To get rid of the fractions, let's multiply all terms by 2:

$2\left(\frac{x^2}{2}\right) - 2x - 2\left(\frac{x}{2}\right) = 0$

Simplify:

$x^2 - 2x - x = 0$

$x^2 - 3x = 0$

Now, factor out the common term:

$x(x - 3) = 0$

Now, set each factor equal to zero and solve for x:

$x = 0$ or $x - 3 = 0$

If $x - 3 = 0$, then $x = 3$.

So the solutions to the equation are $x = 0$ or $x = 3$.

в) $\frac{x - 7}{x - 2} + \frac{x + 4}{x + 2} = 1$

To simplify this equation, let's find a common denominator for the fractions, which is $(x - 2)(x + 2)$:

$\frac{(x}{}$