Question

Simplify the following expression.

Answer 1

Choice A is the answer.

Explanation:

We have given an expression.

2x²+7x+3 / x²-9.

We have to simplify given expression.

Denominator: 2x²+7x+3

Making factors, we have

2x²+7x+3 = 2x²+6x+x+3

2x²+7x+3 = 2x(x+3)+1(x+3)

2x²+7x+3 = (x+3)(2x+1)

Numerator : x²-9

x²-9 = (x)²-(3)²

x²-9 = (x-3)(x+3)

Now,

2x²+7x+3 / x²-9 = (x+3)(2x+1) / (x-3)(x+3)

2x²+7x+3 / x²-9 = 2x+1 / x-3 which is the answer.

Answer 2

For that case, we factor the numerator and denominator:

Numerator:

`2x ^ 2 + 7x + 3`

We rewrite the term of the medium as a sum of two terms whose product is:

`2 * 3 = 6`

And the sum is:

+7

Those numbers are 6 and 1.

`2x ^ 2 + 6x + 1x + 3`

We factor the maximum common denominator of each group:

`2x (x + 3) +1 (x + 3)`

So:

`2x ^ 2 + 7x + 3 = (2x + 1) (x + 3)`

Denominator:

`(x ^ 2-9) = (x + 3) (x-3)`

So, we have:

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

Simplifying we have left:

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

Answer:

Option A