Mathematics: Match the rational expressions to their rewritten form. (match the top to the bottom, zoom in for a clearer picture)

The answer is 5h= nStep-by-step...

Match the rational expressions to their rewritten

arod20061

08.01.2022

Step-by-step explanation:

We have been given Four options we will solve each one so as to write in rational or fractional form

CASE 1:

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

We will simplify by taking LCM we get:

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

After further simplification:

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

Hence, Option 3 matches with 1.

CASE 2:

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

We will simplify by taking LCM we get:

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

After further simplification:

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

Hence, Option 1 matches with 2.

CASE 3:

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

We will simplify by taking LCM we get:

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

After further simplification:

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

Hence, Option 2 matches with 3.

CASE 4:

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

We will simplify by taking LCM we get:

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

After further simplification:

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

Hence, Option 4 matches with 4.

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