**Answer:**

1

**Step-by-step explanation:**

The algebraic expression is

(x²+ 7x+10/ x²+ 4x+4 ) (x²+ 3x+2/x²+ 6x+5)

The options are Arrangement

a.(x+5/x+2) * ( x+2/x+5) Number 2

b.(x+7/x+4) ( x+1/x+2)

c. 1 Number 4

d. (x+5) ( x+2) /(x+5)

e. (x+7) (x+1)/(x+4) ( x+1) * (x+3) (x+1)/(x+3) (x+2)

f. (x+2) (x+5)/(x+2) ( x+2) * (x+1) (x+2)/(x+5) ( x+1) Number 1

g. x+2

h.(x+5/x+2) ( x+2/x+5) Number 3

<u><em>**Answer **</em></u>

Factorizing the expressions (x²+ 7x+10/ x²+ 4x+4 ) (x²+ 3x+2/x²+ 6x+5)

=(x²+ 5x+2x+ 10/ x²+ 2x+2x+4 ) (x²+ 2x+x+ 2/x²+ 5x+x+5)

Taking common

=[x(x+5) +2(x+5)/ x(x+2) +2(x+2) ] [ x(x+2) +1(x+2)/ x((x+5) +1(x+5)]

Putting commons together

=[(x+2) (x+5)/ (x+2) (x+2)] [ (x+2)(x+1)/ (x+1) (x+5)]

Cancelling

= [ (x+5)/ (x+2)]* [ (x+2)/ (x+5)]

=[ (x+5)/ (x+2)] [ (x+2)/ (x+5)]

Again Cancelling

=1

<em><u>**The above question is solved in 4 steps :**</u></em>

Step 1

(x+2) (x+5)/(x+2) ( x+2) * (x+1) (x+2)/(x+5) ( x+1)

Step 2

(x+5/x+2) * ( x+2/x+5)

Step 3

(x+5/x+2) ( x+2/x+5)

Step 4

1 which is the answer .

The steps

(x+7) (x+1)/(x+4) ( x+1) * (x+3) (x+1)/(x+3) (x+2) ,

(x+5) ( x+2) /(x+5),

(x+7/x+4) ( x+1/x+2) and (x+2) are not related to this question.