Subtracting Rational Expressions

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Rational expressions are the expression which consist of constants and variables combined together by addition, subtraction, multiplication or division. The coefficients of the variables (the numbers beside the variables) are usually in the form of fractions. Subtracting rational expressions involves combining the like terms together and if there are fractions involved, we have to make sure that they are of the same denominator. If the rational expressions are not of the same denominator, then we have find their least common denominator and then simplify the expression accordingly.

Example 1: Subtract the given two rational expressions:(5x/6) – (2x/3)

In order to subtract the rational expressions, we have to first find their common denominator.

The LCM of 6 and 3 is 6.

Here the first term, 5x/6 has the denominator as ‘6’ so the term stays the same.

For the second term, multiply the numerator and the denominator by ‘2’ to get the common denominator ‘6’==> (2x* 2)/ (3* 2)= 4x/6

Now, 5x/6 – 4x/6 = (5x- 4x)/6 = x/6.

Example 2: Subtract the given two rational expressions: (3a/2) – (4a/5)

In order to subtract the rational expressions, we have to first find their common denominator.

The LCM of 2 and 5 is 10.

For the first term, multiply the numerator and the denominator by ‘5’ to get the common denominator ‘10’->(3a* 5)/ (2* 5) = 15a/10.

Similarly, for the second term multiply the numerator and the denominator by ‘2’ to get the common
denominator ‘10’==> (4a* 2)/ (5* 2) = 8a/10

Now we have, 15a/10 – 8a/10= (15a- 8a)/10= 7a/10.


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