Question

Алгоритм решения дробных уравнений на примере уравнения х-2/х+1=2х+1/х+25

Answer 1

( Х - 2 ) / ( Х + 1 ) = ( 2х + 1 ) / ( Х + 25 )
( Х + 1 ) не равен 0 ==> Х не равен ( - 1 )
( Х + 25 ) не равен 0 ==> Х не равен ( - 25 )
( Х - 2 )( Х + 25 ) = ( 2х + 1 )( Х + 1 )
Х^2 + 25х - 2х - 50 = 2х^2 + 2х + Х + 1
Х^2 + 23х - 50 = 2х^2 + 3х + 1
2х^2 - х^2 + 3х - 23х + 1 + 50 = 0
Х^2 - 20х + 51 = 0
D = ( - 20 )^2 - 4•51 = 400 - 204 = 196 = 14^2
X1 = ( 20 + 14 ) : 2 = 17
X2 = ( 20 - 14 ) : 2 = 3
Ответ 17 ; 3

Answer 2

Algorithm for Solving Fractional Equations

To solve the fractional equation x - 2/x + 1 = 2x + 1/x + 25, we can follow these steps:

1. Identify the Fractional Equation: The given equation is a fractional equation because it contains fractions or rational expressions.

2. Clear the Fractions: To simplify the equation, we can clear the fractions by multiplying every term by the least common multiple (LCM) of the denominators. In this case, the LCM of the denominators x and (x + 25) is x(x + 25).

3. Solve the Equation: After clearing the fractions, we can solve the resulting equation to find the value of x.

4. Check for Extraneous Solutions: It's important to check the solutions obtained to ensure they are valid for the original equation.

Solution Steps

1. Identify the Fractional Equation: - The given equation x - 2/x + 1 = 2x + 1/x + 25 is a fractional equation due to the presence of fractions and rational expressions.

2. Clear the Fractions: - Multiply every term by the LCM of the denominators, which is x(x + 25): - x(x + 25) * (x - 2/x + 1) = x(x + 25) * (2x + 1/x + 25)

3. Solve the Equation: - After clearing the fractions, simplify the equation and solve for x.

4. Check for Extraneous Solutions: - Verify the obtained solutions by substituting them back into the original equation to ensure they are valid.

Let's proceed with the calculation and solving of the equation.