## Adding or Subtracting Rational Expressions

Adding or Subtracting Rational Expressions

Step 1:- If the denominators are the same, add or subtract the numerators.

Place the result over the common denominator.

If the denominators are different, first find the least common denominator. Write all rational expressions with this LCD, and then add or subtract the numerators. Place the result over the

common denominator.

Step 2:-  Simplify. Write all answers in lowest terms.

## Adding and Subtracting Functions

Adding and Subtracting Functions

If f (x) and g(x) define functions, then

( f + g) (x) = f (x) + g(x) Sum function

and ( f g) (x) = f (x) g(x). Difference function

In each case, the domain of the new function is the intersection of the

domains of f (x) and g(x).

## Adding Real Numbers

Like signs :- To add two numbers with the same sign, add their absolute

values. The sign of the answer (either + or -) is the same as the sign of

the two numbers.

Unlike signs  :- To add two numbers with different signs, subtract the

smaller absolute value from the larger. The sign of the answer is the

same as the sign of the number with the larger absolute value.

## Adding Rational Expressions

Adding Rational Expression with Like Denominators

To add when the denominators are the same, add the numerators and keep the same denominator. Then simplify if possible.

Example

.

To add rational expressions with different denominators:

a. Find the LCM of the denominators. This is the least common

denominator (LCD).

b. For each rational expression, find an equivalent expression with

the LCD. To do so, multiply by 1 using an expression for 1 made up

of factors of the LCD that are missing from the original

denominator.

c. Add the numerators. Write the sum over the LCD.

d. Simplify if possible.

## Adding Using the LCD

Adding Using the LCD

Let’s  finish adding and :

The least common denominator, LCD, is 2 . 2 . 3 . 5. To get the LCD in the first denominator, we need a 5. To get the LCD in the second denominator, we need another 2. We get these numbers by multiplying by form of 1:

Multiplying by 1

= Each denominator is now the LCD.

=     Adding the numerators and keeping the LCD

=  Factoring the numerator and removing a factor of 1: = 1

= .  Simplifying