How do you solve addition of rational expressions?

Answer 1

Answersuppose

Q=

x-5 + 3x+11
____ _______
2x+3 2x+3

Solution :-

SInce there is a common denominator for both expressions : .

It bcomes Single

= x-5+3x+11
_________
2x+3

(add the like terms)

4x+6
____
2x+3

(Take 2 common in the numerator)

2(2x+3)
_______
2x+3

=2

After cancelling 2x+3 from abv and below u get the answer as 2 .

More generally...The above answer only works if the two expressions have the same denominator. What happens if they're not the same? Exactly the same thing as when you're adding fractions (like 3/4 + 2/5). You find a common denominator. Any common multiple will do.

Example:

2x+3 7
--------------- + -----------------
(2x-5)(x+6) (2x-5)(x+4)

You could find a common denominator just by multiplying the two denominators together. Then the denominator would be (2x-5)^2 * (x+6) * (x+4). But, just as with fractions, you can make it easier by using the lowest common multiple instead of the product of the denominators. In this case, (2x-5) * (x+6) * (x+4). Now write the fractions using this denominator:

(2x+3)(x+4) 7(x+6)
---------------------- + ----------------------
(2x-5)(x+6)(x+4) (2x-5)(x+4)(x+6)

=

2x^2 + 11x + 12 7x+42
---------------------- + ----------------------
(2x-5)(x+6)(x+4) (2x-5)(x+4)(x+6)

Then add them as in the answer above:

(2x^2 + 11x + 12) + (7x+42)
--------------------------------------------
(2x-5)(x+6)(x+4)

=

2x^2 + 18x + 54
----------------------
(2x-5)(x+6)(x+4)

If you want, you can rewrite this one as

2(x^2 + 9x + 27)
----------------------
(2x-5)(x+6)(x+4)