Question

(х-2)\(х+3)-30\(х^2-9)=3/8

Answer 1

Ответ на фото///////////////////

Answer 2

To solve the equation $\frac{{(x-2)}}{{(x+3)}} - \frac{{30}}{{(x^2-9)}} = \frac{3}{8}$, we can follow these steps:

Step 1: Simplify the equation. Step 2: Find the common denominator. Step 3: Multiply both sides of the equation by the common denominator to eliminate the fractions. Step 4: Solve the resulting quadratic equation. Step 5: Check the solutions in the original equation to ensure there are no extraneous solutions.

Let's solve the equation step by step:

Step 1: Simplify the equation. The equation becomes: $\frac{{(x-2)}}{{(x+3)}} - \frac{{30}}{{(x-3)(x+3)}} = \frac{3}{8}$

Step 2: Find the common denominator. The common denominator is $(x-3)(x+3)$.

Step 3: Multiply both sides of the equation by the common denominator. 8(x-2)(x+3) - 8 * 30 = 3(x-3)(x+3)

Step 4: Simplify and solve the resulting quadratic equation. 8(x-2)(x+3) - 240 = 3(x-3)(x+3)

Expanding the terms: 8(x^2 + x - 6) - 240 = 3(x^2 - 9)

Simplifying: 8x^2 + 8x - 48 - 240 = 3x^2 - 27

Combine like terms: 8x^2 + 8x - 288 = 3x^2 - 27

Rearrange terms to form a quadratic equation: 5x^2 - 8x - 261 = 0

Now, we need to solve this quadratic equation. We can use factoring, completing the square, or the quadratic formula. Factoring might not be easy for this equation, so let's use the quadratic formula:

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

For the equation 5x^2 - 8x - 261 = 0: a = 5, b = -8, c = -261

Substituting the values into the quadratic formula: x = $\frac{{-(-8) \pm \sqrt{{(-8)^2 - 4(5)(-261)}}}}{{2(5)}}$

Simplifying: x = $\frac{{8 \pm \sqrt{{64 + 5220}}}}{{10}}$ x = $\frac{{8 \pm \sqrt{{5284}}}}{{10}}$ x = $\frac{{8 \pm 2\sqrt{{131}}}}{{10}}$ x = $\frac{{4 \pm \sqrt{{131}}}}{{5}}$

So the solutions are: x = $\frac{{4 + \sqrt{{131}}}}{{5}}$ and x = $\frac{{4 - \sqrt{{131}}}}{{5}}$

Step 5: Check the solutions in the original equation. Substitute each solution back into the original equation and check if both sides are equal.

For x = $\frac{{4 + \sqrt{{131}}}}{{5}}$: (\frac{{\left(\frac{{4 + \sqrt{{131}}}}{{5}}\right)-2}}{{\left(\frac{{4 + \sqrt{{131}}}}{{5}}\right)+3}} - \frac{{30}}{{\left(\frac{{4 + \sqrt{{131