another issuei want to subtract (2a-3) /(a^2-4))-2/(a+2) is good to do (2a-3-2)/(a^2-4-a-2) (subtract up and down)?

2 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should know that the algebraic addition of two fractions is possible if they have common denominators. If they do not have a common denominator, then you need to find it.

In this problem, notice that you may write the first denominator as the special product

Notice that the second denominator needs to be multiplied by to become the denominator of the first fraction.

Considering the order of operations yields:

Hence, evaluating the algebraic expression yields

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

In this case, absolutely not!

When we are adding/subtracting 2 or more fractions, the first step is to check if they have the same denominator.

In this case, they don't have the same denominator.

We'll calculate the least common denominator:

LCD = (a-2)(a+2)

LCD = a^2 - 4

We'll multiply each fraction by LCD:

(2a-3) (a^2 - 4)/(a^2-4) - 2(a^2 - 4)/(a+2)

We'll simplify and we'll get:

2a - 3 - 2(a-2)

We'll remove the brackets:

2a - 3 - 2a + 4

We'll eliminate and combine like terms:

(2a-3) /(a^2-4)-2/(a+2) = 1

The result is not depending on the variable a.