Question

Решите Дробное рациональное уравнение

Answer 1

Решение смотри на фото

Answer 2

Solving a Fractional Rational Equation

To solve a fractional rational equation, we need to find the values of the variable that make the equation true. Let's consider an example equation and solve it step by step.

Example Equation: \( \frac{5}{x} - \frac{9}{x+6} = \frac{53}{x^2 - 152x + 2} \) To solve this equation, we can follow these steps:

1. Find the least common denominator (LCD) of the fractions involved in the equation. In this case, the LCD is \( x(x+6)(x^2 - 152x + 2) \).

2. Multiply every term in the equation by the LCD to eliminate the denominators. This step will help us simplify the equation and solve for the variable.

3. Simplify the equation by distributing and combining like terms.

4. Solve the resulting equation for the variable.

Let's solve the example equation step by step:

Step 1: Find the least common denominator (LCD) The LCD in this case is \( x(x+6)(x^2 - 152x + 2) \).

Step 2: Multiply every term by the LCD Multiplying every term in the equation by the LCD, we get:

\[ x(x+6)(x^2 - 152x + 2) \left( \frac{5}{x} - \frac{9}{x+6} \right) = x(x+6)(x^2 - 152x + 2) \left( \frac{53}{x^2 - 152x + 2} \) \]

Step 3: Simplify the equation After multiplying and simplifying, we get:

\[ 5(x+6)(x^2 - 152x + 2) - 9x(x^2 - 152x + 2) = 53x \]

Expanding and combining like terms, we have:

\[ 5x^3 - 760x^2 + 10x - 912 - 9x^3 + 1368x^2 - 18x = 53x \]

Simplifying further, we get:

\[ -4x^3 + 608x^2 - 28x - 912 = 53x \]

Step 4: Solve for the variable To solve for the variable, we need to bring all the terms to one side of the equation and set it equal to zero:

\[ -4x^3 + 608x^2 - 28x - 912 - 53x = 0 \]

Combining like terms, we have:

\[ -4x^3 + 608x^2 - 81x - 912 = 0 \]

At this point, we can use various methods to solve the cubic equation, such as factoring, synthetic division, or numerical methods. However, without further information or constraints, it is difficult to determine the exact solution to this equation.

Please provide additional information or constraints if you would like a more specific solution to the equation.

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