Consider the following quotients: (4x^2 + 8x + 3) / (2x+1) and 483/21. a. How are these expressions related? b. Find each quotient. c. Explain the connection between the quotients.

a) Put x=10, then the both terms will be same.

b) (2x+3) and 23

c) (2x+3) is a general term for all values of x and 23 is a particular value for x=10

Step-by-step explanation:

a) Considering the following two fractions (4x²+8x+3) / (2x+1) and 483/21, they are equivalent to each other for the value of x = 10.

Therefore, if you put x=10 in the fraction (4x²+8x+3) / (2x+1), then it will become 483/21. (Answer)

b) The quotient of the fraction (4x²+8x+3) / (2x+1) will be obtained by as follows:

(4x²+8x+3) / (2x+1) {By factorizing the numerator}

= (4x²+6x+2x+3) / (2x+1)

= (2x+3) (2x+1) / (2x+1)

=2x+3

Again, the quotient of the fraction 483/21 = 23 (Answer)

c) Again, if you put the value of x = 10 in the quotient (2x+3), then it will result 23. Therefore, (2x+3) is a general term which is valid for all the real values of x and 23 is a particular value for x=10. (Answer)