This week in math class we learned about rational expressions. A rational number is a quotient of two integers (eg. 3/5)
We looked at equivalent fractions, which means fractions that have the same value but are written differently.
We know that 2/3 is equivalent to 6/4 because 6/4 can be reduced to 2/3. It is the same with fractions that involve quadratic or linear equations.
Example:
If we simplify the first fraction, it would eventually reduce to
Non-permissible values
When working with quadratic or linear equations, we have to state the restrictions for the denominator. If a quadratic equation is in the denominator, it must first be factored.
Example:
The quadratic in the denominator can be factored:
Therefore, in the denominator, x cannot be equal to 1 or 2.(x≠1,2)
The reason x cannot equal those values is because they would result in a zero in the denominator, which is not allowed.
Multiplication
Let’s take:
The first step here would be to factor:
$latex \frac{(x-3)(x+2)}{(x+4)}$ ⋅
Once the factoring is done, we have to state the non-permissible values for x: (x≠-4,0,-2) Those are the values in the denominator which x cannot equal.
Then, we can simplify:
Simplifying is just like in numbers, because like factors cancel each other out, or result into a 1, which makes the factors become invisible.
Division.
If given, 1/2÷2/4, most of us would probably know that the second fraction can be reciprocated and then we would simply multiply: 1/2⋅4/2=2/2=1
The same concept is used when dividing fractions involving equations:
$latex