In previous lessons, you learned how to add and subtract rational expressions. We will now extend these
concepts to slightly more difficult expressions.

For any two rational expressions p(x) /qx and r(x)/s(x) where q(x)≠ s(x), their sum is given by

and if q(x)=s(x)

that is, if the rational expressions are of the form p(x)/qx, r(x)/s(x) then

Example 1

Find the sum of

2a²b≠100a³

We first find the LCM of the denominators.

2a²b=2∗a²∗b

100a³=22∗52∗a³

LCM=22∗52∗a³∗b

=100a³b

we get

Example 2

Find the value of

Example 3

Find the sum of (x+2)/(x-2) and (x-2)/(x+2)

Try these questions

Find the values of

1. 




2. 




3. 




4. 




5. 

Answers to the questions

1. To solve      

   Consider q(x)=17x

   s(x)=51x

   =3∗17x

   ∴ LCM of q(x),s(x)=51x

   

   
   

   




2. To solve       

   Consider the denominators

   p(x)=xy

   s(x)=xy³

   u(x)=x²y²

   Irreducible factors x,y

   Highest exponent of factors 2, 3

   ∴ LCM =x²y³

   then

   




3. To solve       

   
   

   a–x≠a+x

   




4. To solve       

   Let q(x)=x²–y²

   s(x) =(x²+xy)

   Factorizing

   q(x) =(x–y)(x+y)

   s(x)=x(x+y)

   Irreducible factors are x, x+y, x–y

   Highest exponents of these factors are 1, 1, 1

   LCM=x(x+y)(x–y)

   
   

   

   




5. To solve      

   Factorizing the numerators and denominators

   

   Canceling like terms in the numerator and denominator of each polynomial.