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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

User Dracstaxi
by
8.3k points

2 Answers

6 votes

Answer:

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.

User Gabriele B
by
8.0k points
3 votes
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)
User Dheeraj Pande
by
8.7k points

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