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# Rational Inequalities Calculator

Inequality is defined as an equation. In inequalities, you use less than, greater than, or not equal instead of an equal sign.

## What is Rational Inequalities Calculator?

'**Rational Inequalities Calculator**' is an online tool that helps to find the value of x for a given inequality. Online Rational Inequalities Calculator helps you to find the value of x for a given inequality in a few seconds.

### Rational Inequalities Calculator

## How to Use Rational Inequalities Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the rational inequality in the given input box.**Step 2:**Click on the**"Solve"**button to find the value of x for a given inequality.**Step 3:**Click on the**"Reset"**button to clear the field and enter new values.

## How to Find Rational Inequalities?

A rational inequality is defined as an inequality such that it can be expressed as the rational expression, quotient, fraction p/q, or simply the quotient of two polynomials. It means both the numerator and denominator are polynomials.

There are different types of inequalities that are greater than(>), less than (<), greater than or equal to(≥), less than or equal to (≤). Rational inequality is a combination of rational expression and inequality.

For example x + 1 / x + 3 is a rational expression. x + 1 / x + 3 <= 5 is rational inequality.

Let us see an example to understand briefly.

**Solved Examples on Rational Inequalities Calculator**

**Example 1:**

Solve the rational inequality x + 5 / x + 3 >= 2

**Solution:**

\(\frac{(x + 5)}{(x + 3)} - 2 >=0\) \(\)[x + 3 is not equal to zero ⇒ x is not equal to -3]

\(\frac{(x + 5 - 2x - 6)}{(x + 3)} >=0\)

\(\frac{(-x - 1)}{(x + 3)} >=0\)

\(-x - 1>=0\\ x + 1<= 0\\ x<=-1\)

⇒ -3 < x <= -1

**Example 2:**

Solve the rational inequality x - 1 / x - 7 <= 5

**Solution:**

\(\frac{(x - 1)}{(x - 7)} - 5 <=0\) \(\)[x - 7 is not equal to zero ⇒ x is not equal to 7]

\(\frac{(x - 1 - 5x + 35)}{(x - 7)} <=0\)

\(\frac{(-4x + 34)}{(x - 3)} <=0\)

\(-4x + 34<=0\\ -4x <= -34\\ 4x>=34\\x>=34/4\\x>=17/2\)

Similarly, you can try the calculator to find the rational inequalities for:

- 5 < = 2x + 5 / x - 5
- x - 5 / 2x + 3 < 2

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