Question

. Find the quotients.
a) (x2 - 4) =/(x + 2)
c) (4x2 - 1) / (2x + 1)​

Answer 1

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

Explanation:

a) (x2 - 4)/(x + 2)

We can simply use factorization to solve the given question.

Here the first term will be numerator and second term will be denominator.

We will factorize the numerator.

So,

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

Using formula,
`a^2+b^2 = (a+b)(a-b)`

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

b) (4x2 - 1) / (2x + 1)​

We can simply use factorization to solve the given question.

Here the first term will be numerator and second term will be denominator.

We will factorize the numerator.

`(4x^2-1)/(2x+1)`

Using formula,
`a^2+b^2 = (a+b)(a-b)`

`= ((2x)^2-(1)^2)/(2x+1)\\=((2x+1)(2x-1))/(2x+1)\\= 2x-1`

Hence,

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