Question

Simplify the complex fraction: 4/(x+3)/(1/x+3) A. 12x+4/x^2+3x. B. 4x/3x+9. C. 4x/3x^2+10x+3. D. None of these

Answer 1

The correct option is C.

Explanation:

The given expression is

`((4)/(x+3))/(((1)/(x)+3))`

`((4)/(x+3))/(((1)/(x)+3))=((4)/(x+3))/((1+3x)/(x))`

The complex faction can be simplified as

`(((a)/(b)))/(((c)/(d)))=(a)/(b)* (d)/(c)`

`((4)/(x+3))/(((1)/(x)+3))=(4)/(x+3)* (x)/(1+3x)`

`((4)/(x+3))/(((1)/(x)+3))=(4x)/((x+3)(1+3x))`

`((4)/(x+3))/(((1)/(x)+3))=(4x)/(x(1+3x)+3(1+3x))`

`((4)/(x+3))/(((1)/(x)+3))=(4x)/(x+3x^2+3+9x)`

`((4)/(x+3))/(((1)/(x)+3))=(4x)/(3x^2+10x+3)`

Therefore the correct option is C.

Answer 2

The answer is C. 4x/3x^2+10x+3


`( (4)/(x+3))/( (1)/(x) +3) = ( (4)/(x+3))/( (1)/(x)+ (3x)/(x)) =( (4)/(x+3))/( (1+3x)/(x) ) = (4)/(x+3)* (x)/(1+3x)= (4x)/((x+3)(1+3x)) = (4x)/(x+3 x^(2) +3+9x)`
`= (4x)/(3 x^(2) +10x+3)`