Question

16/(х+6)(х-1)-20/(х+2)(х+3)=1 Решите,пожалуйста!

Answer 1

16/(x²+5x-6)-20/(x²+5x+6)=1
x²+5x-6=a
16/a-20/(a+12)=1
16a+192-20a-a²-12a=0 
a²+16a-192=0
a1+a2=-16 U a1*a2=-192
a1=-24⇒x²+5x-6=-24
x²+5x+18=0
D=25-72=-47<0 нет решения
a2=8⇒x²+5x-6=8
x²+5x-14=0
x1+x2=-5 U x1*x2=-14
x1=-7 U x2=2 

Answer 2

Problem Statement

We are given the equation:

16/(x+6)(x-1) - 20/(x+2)(x+3) = 1

We need to solve this equation for x.

Solution

To solve the given equation, we will follow these steps:

Step 1: Simplify the equation by finding a common denominator for the fractions.

Step 2: Combine the fractions on the left-hand side of the equation.

Step 3: Solve the resulting equation.

Let's solve the equation step by step.

Step 1: Simplify the Equation

To find a common denominator for the fractions, we need to multiply the denominators together. In this case, the denominators are (x+6)(x-1) and (x+2)(x+3).

The common denominator will be (x+6)(x-1)(x+2)(x+3).

Step 2: Combine the Fractions

Now, let's combine the fractions on the left-hand side of the equation using the common denominator.

The equation becomes:

16(x+2)(x+3) - 20(x+6)(x-1) = (x+6)(x-1)(x+2)(x+3)

Step 3: Solve the Equation

Now, we can solve the resulting equation.

To do this, we will expand the terms on both sides of the equation, simplify, and then solve for x.

Expanding the terms on both sides of the equation:

16(x^2 + 5x + 6) - 20(x^2 + 5x - 6) = (x^2 + 5x + 6)(x^2 + 5x - 6)

Simplifying:

16x^2 + 80x + 96 - 20x^2 - 100x + 120 = x^4 + 10x^3 - 36x^2 + 30x^3 + 300x^2 - 180x - 36x^2 - 360x + 216

Combining like terms:

-4x^2 - 180x + 216 = x^4 + 40x^3 + 264x^2 - 540x + 216

Rearranging the equation:

x^4 + 40x^3 + 268x^2 - 360x = 0

Now, we have a quartic equation. To solve it, we can factor out x as a common factor:

x(x^3 + 40x^2 + 268x - 360) = 0

From here, we can see that x = 0 is one solution.

To find the other solutions, we can use numerical methods or a graphing calculator.

Therefore, the solutions to the equation are x = 0 and the other solutions can be found using numerical methods or a graphing calculator.

Note: The other solutions may not have simple algebraic expressions.

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