Question

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

Answer 1

Answer:

$\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1$

Step-by-step 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,

$\frac{x^2-4}{x+2}$

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

$\frac{x^2-4}{x+2}\\= \frac{(x^2)-(2)^2}{x+2}\\=\frac{(x+2)(x-2)}{x+2}\\= x-2$

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.

$\frac{4x^2-1}{2x+1}$

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

$= \frac{(2x)^2-(1)^2}{2x+1}\\=\frac{(2x+1)(2x-1)}{2x+1}\\= 2x-1$

Hence,

$\frac{x^2-4}{x+2} = x-2\\\frac{4x^2-1}{2x+1} = 2x-1$