Question

Which expression is equivalent to (x+1)^2-9/x+4

x – 2
x + 2
x – 4
x + 4

Answer 1

Choice A is correct.

Explanation:

We have given the expression:

(x+1)²-9/x+4

We have to simplify the expression.

As we know that :

(x+y)²=x²+y²+2xy

So, we use this formula in the nominator we get,

(x²+1+2x)-9/x+4

x²+1+2x-9/x+4

x²+2x-8/x+4

We have to split the middle term in the nominator such that the sum of two numbers is 2 and the product is -8x² that is +4x and -2x. we get,

x²+4x-2x-8/x+4

(x+4)(x-2)/(x+4)

(x-2) is the answer.

Choice A is correct.

Answer 2

Answer: First option

Explanation:

By definition:

`(a+b)^2=a^2+2ab+b^2`

Then, you can simplify the numerator as following:

`((x+1)^2-9)/((x+4))=(x^2+2x+1-9)/((x+4))=(x^2+2x-8)/((x+4))`

Factor the numerator. Find two number whose sum is 2 and whose product is -8. THese would be 4 and -2. Then:

`=((x+4)(x-2))/((x+4))`

Simplify. Then you obtain:

`x-2`