We are asked to simplify
the given rational expressions.
It's important to remember
when simplifying rational expressions
we cannot simplify across
addition or subtraction.
For example here, it may be
tempting to try to simplify
the negative 12 and three,
but we cannot do this
because we cannot simplify
across this addition.
When simplifying rational expressions,
we simplify the numerator
and denominator completely
then perform the division
indicated by the fraction bar.
If it's helpful, we can
think of having parentheses
around the numerator and denominator.
Simplifying the numerator,
we begin by simplifying
the square root of nine.
The square root of nine is equal to three
because nine is equal three times three
or if you want three squared.
And the square root of three squared
is equal to one factor of three.
And therefore this simplifies
to the quantity negative 12
plus three divided by three.
Still simplifying in the numerator,
negative 12 plus three is
equal to negative nine.
Giving us negative nine divided by three
and now we perform the division,
negative nine divided by three
is equal to negative three.
The given expression
simplifies to negative three.
Looking at the next expression,
again we cannot simplify
the 30 and the 10 here,
because we cannot simplify
across this subtraction.
So again, if it's helpful,
we can think of having parentheses
around the numerator and denominator.
Simplifying the numerator,
we begin by simplifying
the square root of 100.
The square root of 100 is equal to 10
because 100 is equal to 10 times 10.
Or if you want 10 squared,
and the square root of 10 squared
is equal to one factor of 10.
The expression simplifies
to the quantity 30 minus 10 divided by 10.
Still simplifying in the numerator,
30 minus 10 is 20.
Which gives us 20 divided by 10.
20 divided by 10 is equal to two.
The given expression simplifies to two.
I hope you found this helpful.
