Question

1/x+1<1/x-1 решение нужно срочно помогите пожалуйста

Answer 1

1/x+1<1/x-1, x≠0
1<-1 
x ∈ ∅

Answer 2

Solving the Inequality 1/x + 1 < 1/x - 1

To solve the inequality 1/x + 1 < 1/x - 1, we can start by finding the common denominator and then simplifying the expression.

First, let's find the common denominator for the fractions. The common denominator for 1/x and 1 is x. Therefore, we can rewrite the inequality as:

x/x + 1/x < x/x - 1

Simplifying further, we get:

1 + 1/x < 1 - 1/x

Now, let's add -1 to both sides of the inequality:

1 + 1/x - 1 < 1 - 1/x - 1

This simplifies to:

1/x < -1/x

Now, let's multiply both sides by x to get rid of the fractions:

x * (1/x) < x * (-1/x)

This simplifies to:

1 < -1

However, it's important to note that there is no solution to this inequality. This is because the left-hand side of the inequality is always positive (since x is in the denominator), and the right-hand side is always negative. Therefore, there are no values of x that satisfy the given inequality.

This means that the original inequality 1/x + 1 < 1/x - 1 has no solution.