ADDITION OF FRACTION WITH EQUAL/SAME DENOMINATOR                                                                                                                                                                                                                                                                                 x

If algebraic fraction has the same denominator such as ------- and

z

y

z

x               y              x + y

---------- + ---------- = -----------

z               z                z

there are some examples are given below for your better understanding –

8             5

Example.1)  --------- + --------

7x            7x

8 + 5

=  ----------

7x

(After doing LCM of denominator of given fraction we find 7x )

13

=  -----------        (Ans.)

7x

9x             12y

Example.2)  ---------- + ----------

8a              8a

9x + 12y

=  ----------------

8a

(After doing LCM of denominator of given fraction we find 8a )

3 (3x + 4y)

=  ---------------            (Ans.)

8a

ADDITION OF FRACTION WITH DIFFERENT DENOMINATOR -

To add or subtract algebraic fractions that do not have the same denominator, first we have to find the LCM of their denominators and then proceed as in arithmetic.

w             y           (w X z) + (y X x)            wz + yx

-------- + -------- = ------------------- = -------------

x             z                (x X z)                     xz

8              5

Example.1)   --------- + ---------

7x            7y

8.x  +  5.y

=  -------------------

7xy

(After doing LCM of denominator of given fraction we find 7xy)

8x + 5y

=  -------------        (Ans.)

7xy

9a            7b

Example.2)  --------- + --------

8x            4y

(9a . y) +  (7b . 2x)

=  -----------------------

8xy

(After doing LCM of denominator of given fraction we find 8xy)

9ay + 14bx

=  --------------         (Ans.)

8xy