Question

9/x-2- 5/x=2 /-дробная черта

Answer 1

Ответ:  x₁=5       x₂=-1.

Объяснение:

(9/(x-2))-(5/x)=2     x-2≠0   x≠2    x≠0

9*x-5*(x-2)=2*x*(x-2)

9x-5x+10=2x²-4x

4x+10=2x²-4x

2x²-8x-10=0  |÷2

x²-4x-5=0     D=36    √D=6

x₁=5          x₂=-1.

Answer 2

To solve the equation (9/x) - (2 - 5/x) = 2, we'll follow these steps:

Step 1: Simplify the equation. Step 2: Get rid of fractions by multiplying each term by the common denominator. Step 3: Solve for x.

Let's proceed with the solution:

Step 1: Simplify the equation. (9/x) - (2 - 5/x) = 2

Step 2: Get rid of fractions. The common denominator for the terms involving x is x. So, we'll multiply each term by x to eliminate the fractions.

x * (9/x) - x * (2 - 5/x) = x * 2

Simplifying further:

9 - x * (2 - 5/x) = 2x

Step 3: Solve for x. Expand the term on the left side:

9 - (2x - 5) = 2x

Now, combine like terms:

9 - 2x + 5 = 2x

Subtract 2x from both sides:

9 + 5 = 2x + 2x

14 = 4x

Finally, divide both sides by 4 to solve for x:

x = 14 / 4 x = 3.5

So, the solution to the equation is x = 3.5.