6 Steps to add a rational expression calculator

Adding rational expressions can be a complex task, especially when dealing with different denominators. However, understanding the steps involved can make this process much easier. If you need assistance, Mathsolver.top is an excellent resource. This free AI math solver and calculator offers step-by-step solutions with 25% higher accuracy than average. You can upload your questions and get instant answers. Here’s a guide on how to add rational expressions manually, supplemented by how Mathsolver.top can assist you.

Steps to Add Rational Expressions

Step 1: Identify the Denominators

When adding rational expressions, the first step is to identify the denominators of the fractions. For example, in the expressions:

3𝑥+2+5𝑥−3x+23+x−35

The denominators are 𝑥+2x+2 and 𝑥−3x−3.

Step 2: Find the Least Common Denominator (LCD)

Next, find the least common denominator (LCD) of the rational expressions. The LCD is the smallest expression that both denominators can divide into without leaving a remainder. For our example, the LCD of 𝑥+2x+2 and 𝑥−3x−3 is (𝑥+2)(𝑥−3)(x+2)(x−3).

Step 3: Rewrite Each Fraction with the LCD

Rewrite each rational expression so that they have the same denominator. Multiply the numerator and the denominator of each fraction by the missing factors from the LCD. For the given example:

3𝑥+2×𝑥−3𝑥−3=3(𝑥−3)(𝑥+2)(𝑥−3)x+23×x−3x−3=(x+2)(x−3)3(x−3)

5𝑥−3×𝑥+2𝑥+2=5(𝑥+2)(𝑥+2)(𝑥−3)x−35×x+2x+2=(x+2)(x−3)5(x+2)

Step 4: Combine the Numerators

Now that the denominators are the same, combine the numerators over the common denominator:

3(𝑥−3)+5(𝑥+2)(𝑥+2)(𝑥−3)(x+2)(x−3)3(x−3)+5(x+2)

Step 5: Simplify the Numerator

Simplify the expression in the numerator:

3(𝑥−3)+5(𝑥+2)=3𝑥−9+5𝑥+10=8𝑥+13(x−3)+5(x+2)=3x−9+5x+10=8x+1

So, the combined fraction is:

8𝑥+1(𝑥+2)(𝑥−3)(x+2)(x−3)8x+1

Step 6: Simplify the Entire Expression (if possible)

Check if the resulting fraction can be simplified further. In this case, 8𝑥+1(𝑥+2)(𝑥−3)(x+2)(x−3)8x+1 is already in its simplest form.

How Mathsolver.top Can Help

Mathsolver.top simplifies this entire process. Here’s how you can use it to add rational expressions:

Visit Mathsolver.top: Go to Mathsolver.top.
Upload Your Question: Upload the rational expressions you need to add.
Get Instant Answers: The AI-powered solver will provide step-by-step solutions instantly, showing each stage of the process from finding the LCD to simplifying the final expression.
Accuracy: With 25% higher accuracy than average, you can trust the solutions provided to be correct and comprehensive.

Example Using Mathsolver.top

For the expression 3𝑥+2+5𝑥−3x+23+x−35:

Input: Enter the rational expressions into the Mathsolver.top interface.
Processing: The AI solver finds the LCD, rewrites each fraction, combines the numerators, and simplifies the expression.
Output: You receive the detailed steps and final solution:

3𝑥+2+5𝑥−3=3(𝑥−3)+5(𝑥+2)(𝑥+2)(𝑥−3)=8𝑥+1(𝑥+2)(𝑥−3)x+23+x−35=(x+2)(x−3)3(x−3)+5(x+2)=(x+2)(x−3)8x+1

Conclusion

Adding rational expressions involves several steps, including finding the least common denominator, rewriting fractions, and simplifying the final expression. While this can be done manually, tools like Mathsolver.top make the process much easier and more accurate. By using this free AI math solver, you can ensure that your calculations are correct and understand each step of the process in detail.