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
Answer
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
The above question is solved in 4 steps :
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.
