Question

What must be true of two rational expressions before they can be added?

Answer 1

Answer:

They most have common denominators.

Step-by-step explanation:

Let the following two rational expressions:

$\frac{p}{a} , \frac{q}{b}$

where p,a,q, b are integers, a and b the denominators are not 0, i.e. $a,b\neq 0$

We can add rational expressions only if their denominator is same.

That is why we find LCD to be $ab$.

Then,

$\frac{p}{a} +\frac{q}{b} =\frac{pb+qa}{ab}$

Let the following two rational expressions:

$\frac{p}{a} , \frac{q}{b}$

where p,a,q, b are integers, a and b the denominators are not 0, i.e. $a,b\neq 0$

We can add rational expressions only if their denominator is same.

That is why we find LCD to be $ab$.

Then,

$\frac{p}{a} +\frac{q}{b} =\frac{pb+qa}{ab}$

So, the correct answer is the last option that we can sum rational expressions if they have common denominator.