Question

What is the sum of the rational expressions below?

Answer 1

Answer: OPTION B.

Explanation:

Given the rational expressions
`(3x+2)/(x-1)` and
`(2x-5)/(x-1)`, we can observe that both have the same denominator, then we can add them.

We must rewrite the denominator
`x-1` and add the numerators. Then:

`=((3x+2)+(2x-5))/(x-1)`

Therefore, adding the like terms on the numerator, we get the following sum:

`=(5x-3)/(x-1)`

We can observe that this sum matches with the sum shown in the option B.

Answer 2

For this case we have that the fractions have the same denominator, then we can rewrite as:

`\frac {3x + 2 + (2x -5)} {x-1} =`

We eliminate the parenthesis:

`+*+=+`

`+*-=-`

`\frac {3x + 2 + 2x - 5} {x-1} =`

We add common terms of the numerator:

`\frac {5x-3} {x-1}`

Thus, the correct expression is option B.

Answer:

Option B