Question

X/x-3 + 3/x-2= 3/x^2-5x+6 1-x/x-4 + 3/3-x= 3/x^2-7x+12 помогите решить пожалуйста не понял тему

Answer 1

а) х/(x-3) + 3/(x-2)= 3/(x ²-5x+6)
учтём, что (x ²-5x+6) = (х-3)(х -2) и умножим обе части уравнения на это выражение (освободимся от дробей)
получим:
х(х -2) + 3 (х -3) = 3     х-2≠0,  х-3 ≠ 0
х² -2х +3х -9 -3 = 0
х² -х -12 = 0
х₁ = -3  и  х₂ = 4
Ответ:  х₁ = -3  и  х₂ = 4
(1-x)/(x-4) + 3/(3-x)= 3/(x²-7x+12)
учтём, что (x ²-7x+ 12) = (х-3)(х -4) и умножим обе части уравнения на это выражение (освободимся от дробей), сменим знак перед 2-й дробью.
получим:
(1 - х)( х -3) -3( х - 4 ) = 3           х -3 ≠0,  х - 4 ≠0
х - х² -3 +3х -3х +12 -3 = 0
-х²+х +6 = 0
х² - х - 6 = 0
х₁ = -2  и  х₂ = 3(посторонний)
Ответ: -2

Answer 2

Solving the Equation

To solve the given equation, we'll start by simplifying both sides of the equation and then finding the common denominator. After that, we'll solve for the variable.

The given equation is: X/x-3 + 3/x-2 = 3/x^2-5x+6 + 1-x/x-4 + 3/3-x = 3/x^2-7x+12

Simplifying the Equation

First, let's simplify the equation by finding the common denominator for each fraction.

The common denominator for the fractions on the left-hand side is (x-3)(x-2). The common denominator for the fractions on the right-hand side is (x-4)(3-x).

Combining the Fractions

After finding the common denominators, we'll combine the fractions on both sides of the equation.

Solving for X

Once the fractions are combined, we'll solve for the variable X.

Let's proceed with these steps to solve the equation.