Rational expression is an algebraic expression written in p(x) / q(x) form. The condition for the rational expression is the denominator cannot be equal to zero i.e. q(x) ≠ 0. There are many question related to simplifying given rational expressions. The rational equation can be solved and simplified using different mathematical properties such as multiplicative property, associative property, additive inverse multiplicative inverse and many more.
Example 1: Find the answer for the expression x /5 + 2 x/5 + 3 x/5?
The given question is on adding rational expressions.
This question contains the adding the expressions with same denominator 5
Adding the numerators of the expressions gives (x+ 2 x+ 3 x)/5 = 6 x/5
This makes the solution equal to x/5 + 2x/5 + 3 x/5 = 6 x/5
Example 2: Find the answer for the expression (3 x/ 5) + (x /3) – (4 x/15)?
The given question is on adding and subtracting rational expression.
This question contains the adding and subtracting with different denominator.
The common denominator need to be found for 3, 5 and 15.
The least Common denominator LCM = 15.
Adding the first two terms (3 x/ 5) + (x /3) = (9 x/ 15) + (5x /15) =14 x/15
Now subtract 3 x/15 from the previous answer 14 x/5
(14 x/ 15) - (4 x /15) = (10 x/ 15)
Further simplifying the fraction gives 2 x/3.
This makes the solution equal to (3 x/ 5) + (x /3) – (4 x/15) = 2 x/3.