This is a process by which the denominator terms can be taken to the numerator in an equation. The basic idea is if

Like terms are those that have the same variables, whereas unlike terms have different variables. Like terms can be combined together and so simplified whereas unlike terms cannot be combined. Simplification is very simple if we combine like terms.

For example:

x + 2x = 3x

3a - 4a = -a

6xy - 6xy = 0

### Examples on Simplifying Equations

Given below are some examples on simplifying equations.

**Example 1:**

Simplify 6a + 4xy - 7yx + 5a = 0

**Solution:**

Here, there are four terms of which 6a and 5a are like terms. So, they can be combined.

Now, xy = yx (Since, multiplication is commutative.)

And so, 4xy and 7xy becomes like terms.

So, 7yx = 7xy

6a + 4xy - 7yx + 5a = 0

6a + 4xy - 7xy + 5a = 0

(6a + 5a) + (4xy - 7xy) =0

(11a) + (-3xy) = 0

11a - 3xy = 0

Another important rule that the operation has to follow is called in short as **PEMDAS**. It is a short form for order of operations.

**P** – Parenthesis

**E **– Exponents

**MD** – multiplication or division

**AS** – addition or subtraction

According to the rule, in any equation first do the parenthesis then the exponent, if any. Operations has to performed from left to right with multiplication or division, which ever comes first and addition or subtraction, which ever comes first.

**Example 2:**

Simplify 7x + (6x × 5^{2} + 3x)=0

**Solution:**

Here, start with parenthesis

(6x × 5^{2 }+ 3x)

In that, take the exponent first

5^{2} = 25

So (6x × 5^{2 }+ 3x) = (6x × 25 + 3x)

(6x × 5^{2} + 3x) = (6x × 25 + 3x)

= (150x + 3x)

= 153x

7x + (6x × 5^{2} + 3x)=0

7x + 153x = 0

160x = 0