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A rational expression is a fraction in which either the numerator, or the denominator, or both the numerator and the denominator are algebraic expressions.

### Subtracting Rational Expressions with Same Denominators

**How to subtract rational expressions with same denominators?**

Example:

(8f - g)/2 - (8f + g)/2

**How to add and subtract rational expressions with the the same denominators?**

Examples:

1. (4x - 1)/(x - 3) + (1 + 3x)/(x - 3) =

2. (x^{2} + 7x)/(x - 7) - (10x + 28)/(x - 7) =

### Subtracting Rational Expressions with Different Denominators

**How to subtract rational expressions with different denominators?**

Example:

(-7f)/(f - n) - (4f - n)/(4f - 4n) =

**How to subtract rational expressions with different trinomial denominators?**

Example:

(3q + 4)/(3q^{2} + 5q - 28) - (5q + 3)/(2q^{2} + 3q - 20)
**How to add and subtract rational expressions when the denominators are different?**

Examples:

3/(x - 3) + 2/(x + 5)

7/(x + 2) - 5/(x + 3)

**How to subtract rational expressions with unlike denominators?**

(2x + 5)/(x^{2} + 3x -10) - 3/(x + 6)

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Algebra Lessons

A rational expression is a fraction in which either the numerator, or the denominator, or both the numerator and the denominator are algebraic expressions.

In this lesson, we will be looking at how to subtract rational expressions with the same denominator and rational expressions with different denominators.

When the denominators of two algebraic fractions are the **same**, we can subtract the numerators and then simplify when possible.

* Example: *

Simplify the following expression:

* Solution: *

Example:

(8f - g)/2 - (8f + g)/2

Examples:

1. (4x - 1)/(x - 3) + (1 + 3x)/(x - 3) =

2. (x

When the denominators of two algebraic fractions are **different**, we need to find the Least Common Multiple of the denominators (or LCD) before we subtract the fractions.

Here are the steps you need to follow:

**Step 1: **Find the LCD

** Step 2: ** Express each fraction with the LCD as the denominator.

** Step 3:** Subtract the numerators and simplify when possible.

Now we apply the above 3 steps in the following example.

* Example: *

Express the following as a fraction with a single denominator:

* Solution: *

Example:

(-7f)/(f - n) - (4f - n)/(4f - 4n) =

Example:

(3q + 4)/(3q

Examples:

3/(x - 3) + 2/(x + 5)

7/(x + 2) - 5/(x + 3)

(2x + 5)/(x

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