Question

Упростите неравенство.

Answer 1

$\frac{a}{a+b} - \frac{b}{b-a} - \frac{2ab}{a ^{2}-b ^{2} } =\frac{a}{a+b} +\frac{b}{a-b} - \frac{2ab}{a ^{2}-b ^{2} } = \frac{a ^{2} -ab+ab+b ^{2} -2ab}{a ^{2}-b ^{2} } = \\ \frac{a ^{2} -2ab+b ^{2} }{a ^{2}-b ^{2} } = \frac{(a-b) ^{2} }{(a -b)(a+b)}= \frac{a-b}{a+b}$

Answer 2

Simplifying an Inequality

To simplify an inequality, we need to manipulate the expression to isolate the variable on one side of the inequality symbol. Here's a general process for simplifying an inequality:

1. Identify the inequality symbol: The inequality symbol can be greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤).

2. Simplify the expression: Manipulate the expression to isolate the variable on one side of the inequality symbol. This may involve performing operations such as addition, subtraction, multiplication, or division on both sides of the inequality.

3. Solve for the variable: Once the variable is isolated, solve for its value. This may involve further simplification or solving an equation.

4. Determine the solution set: Express the solution as a range or interval, depending on the context of the problem.

Now, let's apply these steps to an example inequality.

Example: Simplify the inequality 2x + 3 > 7.

1. Identify the inequality symbol: The inequality symbol in this example is greater than (>).

2. Simplify the expression: To isolate the variable, we need to subtract 3 from both sides of the inequality: 2x + 3 - 3 > 7 - 3 2x > 4

3. Solve for the variable: To solve for x, we divide both sides of the inequality by 2: (2x)/2 > 4/2 x > 2

4. Determine the solution set: The solution to the inequality is x > 2, which means that x can take any value greater than 2.

Please note that this is a general process for simplifying an inequality. The specific steps may vary depending on the given inequality. If you have a specific inequality you would like me to simplify, please provide the details, and I'll be happy to assist you further.