Answer:
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:
[tex](x-2)+\frac{6}{x-2}[/tex]
We will simplify by taking LCM we get:
[tex]\frac{(x-2)^2+6}{x-2}[/tex]
After further simplification:
[tex]\frac{x^2-4x+10}{x-2}[/tex]
Hence, Option 3 matches with 1.
CASE 2:
[tex](x+3)+\frac{10}{x-2}[/tex]
We will simplify by taking LCM we get:
[tex]\frac{(x-2)(x+3)+10}{x-2}[/tex]
After further simplification:
[tex]\frac{x^2+x+4}{x-2}[/tex]
Hence, Option 1 matches with 2.
CASE 3:
[tex](x+1)+\frac{6}{x-2}[/tex]
We will simplify by taking LCM we get:
[tex]\frac{(x-2)(x+1)+6}{x-2}[/tex]
After further simplification:
[tex]\frac{x^2-x+4}{x-2}[/tex]
Hence, Option 2 matches with 3.
CASE 4:
[tex](x-3)+\frac{10}{x-2}[/tex]
We will simplify by taking LCM we get:
[tex]\frac{(x-2)(x-3)+10}{x-2}[/tex]
After further simplification:
[tex]\frac{x^2-5x+16}{x-2}[/tex]
Hence, Option 4 matches with 4.
