Question

Дробно рациональные уравнения Решить: числитель. 3х-2 - 2х+3 = 12х+4 Знаменатель. х-1 - х+3 = +2х-3 пожалуйста поподробнее

Answer 1

(3x-2)/(x-1)-(2x+3)/(x+3)=(12x+4)/(x^2+2x-3)

(3x^2+7x-6)/(x^2+2x-3)-(2x^2+x-3)/(x^2+2x-3)=(12x+4)/(x^2+2x-3)

x не равно 1

x не равно -3

x^2+6x-3=12x+4

x^2-6x-7=0

По теореме Виета:

x1=7

x2=-1

Ответ: 7; -1

Answer 2

Solving the Fractional Rational Equation

To solve the given fractional rational equation, we need to find the value of the variable that satisfies the equation. Let's break down the equation and solve it step by step.

The equation is:

Numerator: 3x - 2 - 2x + 3 = 12x + 4

Denominator: x - 1 - x + 3 = 2x - 3

Simplifying the Equation

First, let's simplify the equation by combining like terms on both sides.

Numerator: 3x - 2 - 2x + 3 = 12x + 4 (x + 1) = 12x + 4

Denominator: x - 1 - x + 3 = 2x - 3 2 = 2x - 3

Solving the Numerator

To solve the numerator, we'll isolate the variable on one side of the equation.

(x + 1) = 12x + 4

Let's simplify the equation further:

x + 1 = 12x + 4

Now, let's move all the terms with x to one side and the constant terms to the other side:

x - 12x = 4 - 1

Simplifying further:

-11x = 3

Dividing both sides by -11:

x = -3/11

Solving the Denominator

To solve the denominator, we'll isolate the variable on one side of the equation.

2 = 2x - 3

Let's simplify the equation further:

2x - 3 = 2

Now, let's move all the terms with x to one side and the constant terms to the other side:

2x - 2x = 3 + 2

Simplifying further:

0 = 5

Conclusion

After solving the equation, we found that the denominator equation leads to an inconsistency (0 = 5), which means there is no solution for the given equation.

However, the numerator equation has a solution:

x = -3/11

Therefore, the solution to the given fractional rational equation is x = -3/11.

Please note that the denominator equation does not have a solution, which means the original equation as a whole does not have a solution.

I hope this explanation helps! Let me know if you have any further questions.