Question

Please answer correctly!!!!!!!!

Answer 1

QUESTION 1

The given expression is

$(x-2)+\frac{6}{x-2}$

We collect LCM to get,

$\frac{(x-2)(x-2)+1(6)}{x-2}$

We expand bracket to get,

$\frac{x^2-2x-2x+4+6}{x-2}$

We simplify to get,

$\frac{x^2-4x+10}{x-2}$

Therefore

$(x-2)+\frac{6}{x-2}\rightarrow \frac{x^2-4x+10}{x-2}$

QUESTION 2

The given expression is

$(x+3)+\frac{10}{x-2}$

We collect LCM to get,

$\frac{(x+3)(x-2)+1(10)}{x-2}$

We expand bracket to get,

$\frac{x^2-2x+3x-6+10}{x-2}$

We simplify to get,

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

Therefore

$(x+3)+\frac{10}{x-2}\rightarrow \frac{x^2+x+4}{x-2}$

QUESTION 3

The given expression is

$(x+1)+\frac{6}{x-2}$

We collect LCM to get,

$\frac{(x+1)(x-2)+1(6)}{x-2}$

We expand bracket to get,

$\frac{x^2+x-2x-2+6}{x-2}$

We simplify to get,

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

Therefore

$(x+1)+\frac{6}{x-2}\rightarrow \frac{x^2-x+4}{x-2}$

QUESTION 4

The given expression is

$(x-3)+\frac{10}{x-2}$

We collect LCM to get,

$\frac{(x-3)(x-2)+1(10)}{x-2}$

We expand bracket to get,

$\frac{x^2-2x-3x+6+10}{x-2}$

We simplify to get,

$\frac{x^2-5x+16}{x-2}$

Therefore

$(x-3)+\frac{10}{x-2}\rightarrow \frac{x^2-5x+16}{x-2}$

Answer 2

Answer:

Please, see the attached files.

Step-by-step explanation:

Please, see the attached files.

Thanks.