Question

Which of the following expressions gives a + 5 as its simplest form?
A. (a^2+6a+5)/(a+1)
B. (a+1)/(a^2+6a+5)
C. (a^2-6a+5)/(a-1)
D. (a-1)/(a^2-6a+5)

Answer 1

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Answer 2

Given :    Rational Expressions

To Find : Which of the following expressions gives a + 5 as its simplest form

A. (a²+6a+5)/(a+1)

B. (a+1)/(a²+6a+5)

C. (a²-6a+5)/(a-1)

D. (a-1)/(a²-6a+5)

Solution:

a²+6a+5

Using Middle term split

= a² + 5a + a + 5

= a (a + 5) + 1(a + 5)

= (a + 1) (a + 5)

a²-6a+5

Using Middle term split

= a² - 5a - a + 5

= a (a -5) - 1(a + 5)

= (a - 1) (a- 5)

A. (a²+6a+5)/(a+1)   =  (a + 1)(a + 5)/(a + 1)  = a + 5

Hence Gives desired result

so option A) is correct

B. (a+1)/(a²+6a+5)   = (a + 1) /(a + 5)(a + 1)  =  1/(a + 5) ≠ a + 5

C. (a²-6a+5)/(a-1)  = (a - 1)(a - 5) / (a - 1)  =  a - 5 ≠ a + 5

D. (a-1)/(a²-6a+5) = (a - 1)/ (a - 5)(a - 1)  = 1/(a - 5)  ≠ a + 5

Hence Correct option is  A)  (a²+6a+5)/(a+1)   only.

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