Learn how to simplify fractions with variables from the experts.

Algebraic fractions

An‌ ‌algebraic‌ ‌fraction‌ ‌is‌ ‌a‌ ‌fraction‌ ‌with‌ ‌algebraic‌ ‌expressions‌ ‌in‌ ‌the‌ ‌numerator‌ ‌and‌ ‌denominator.‌

Top things to learn under Algebraic Fractions from the online tutor

Algebraic expressions are usually not a pleasant sight in the Math book. To top that, watching them come in the numerator and denominator making a complex fraction can be mind-boggling.

Learning the right techniques can not only help you deal with algebraic fractions but also make the problems super interesting to solve. 

Here’s what our online tutors will train you for:
 

• Reducing an algebraic fraction to lowest terms
• Adding/Subtracting algebraic fractions
• Multiplying algebraic fractions
• Dividing algebraic fractions
• Understanding rational and irrational fractions

Frequently Asked Questions:

Question 1: How to do algebraic fractions?
Algebraic fractions are fractions that have algebraic expressions in the numerator and/or denominator, and the denominator can never equal 0.

We find the fraction with the smallest common denominator among all the others in the equation.

Multiply the LCD by both sides of the equation. The fractions are now obvious.

On one side, isolate the variable terms, and on the other, isolate the constant terms. Both sides should be simplified.

To make the variable's coefficient equal to one, we use the multiplication or division property.

Question 2: How to solve algebraic equations with fractions?
First, find the fraction with the smallest common denominator among all the others in the equation.

Multiply the LCD by both sides of the equation. The fractions are now obvious.

On one side, isolate the variable terms, and on the other, isolate the constant terms. Both sides should be simplified.

To make the variable's coefficient equal to one, we use the multiplication or division property.

Question 3: How to multiply algebraic fractions?
To multiply algebraic fractions, we multiply the numerators together and denominator numbers together, then simplify the solution for required answers.

Example:

2x+x21+x(1+x)2x+2

= x(x+2)(1+x)2(1+x)(x+2)=x(1+x)

Question 4: How to divide algebraic fractions?
To divide the algebraic fractions, we take the reciprocal of the second term and change the division symbol to a multiplication sign.

After that ,factorize the denominators and numerators together.Remove the components that appear in both the numerator and the denominator.And to get the answer, multiply the two numbers together.

Example:

x2 - 25x - 4x - 5x2 -16=x2 - 25x - 4x2 - 16x -5

   =(x-5)(x+5)(x-4)(x+4)(x-4)(x-5)=(x+5)(x+4)

Question 5: How to add algebraic fractions?
To add algebraic fractions, we first find the denominators' lowest common multiple of given expressions.All fractions should be expressed in terms of the lowest common denominator.To get the solution, we simplify the numerators.

Example

x-2x+1x2=x(x-2)+1x.x2=x2-2x+1x3

Math Tutoring Topics