Simplify each sum or difference. State any restrictions on the variable.
a + 11 a - 21
-------- (Over) + ----------
3a - 5 3a - 5
Trying to type fractions using our format results in a jumbled-up mess like above.
Try it like this:
(a + 11)/(3a-5) + (a - 21)/(3a-5) , hoping this is what you meant.
Since we already have a common denominator, just add up the top.
=( a+11 + a-21)/(3a-5)
= (2a - 10)/(3a - 5)
To simplify the given sum or difference, we need to combine the two fractions into a single fraction. To do this, we need a common denominator for the two fractions, which in this case is (3a - 5).
The first fraction is (a + 11) / (3a - 5), and the second fraction is (a - 21) / (3a - 5).
To add or subtract fractions, we need the same denominator. In this case, since both fractions have the same denominator (3a - 5), we can simply combine the numerators over the common denominator.
The combined fraction is:
((a + 11) + (a - 21)) / (3a - 5)
Now, let's simplify the numerator by combining like terms:
(a + 11 + a - 21) / (3a - 5)
Combining like terms, we get:
(2a - 10) / (3a - 5)
Now, we have simplified the given sum or difference. The simplified expression is (2a - 10) / (3a - 5).
As for the restrictions on the variable (a), we need to look out for any values that make the denominator equal to zero, as division by zero is undefined. Therefore, to find restrictions, we set the denominator to zero and solve for a:
3a - 5 = 0
3a = 5
a = 5/3
Therefore, the only restriction for the variable a is a ≠ 5/3. In other words, any value of a can be used except a value of 5/3.