3+(2x/x+4) divide x/x+4
please simplify the complex fraction thank you show work
2 x / x = 2
x / x = 1
[ 3 + ( 2 x / x + 4 ) ] / ( x / x + 4 )=
( 3 + 2 + 4 ) / ( 1 + 4 ) = 9 / 5
Or, assuming the usual carelessness with parentheses,
(3+(2x/(x+4))) / (x/(x+4))
(3(x+4)+2x)/(x+4) / (x/(x+4))
(3x+12+2x)/x
(5x+12)/x
5 + 12/x
Or even
(3+2x)/(x+4) / x/(x+4)
(3+2x)/x
Or,
3 + (2x/(x+4)) / (x/(x+4))
3 + 2x/x
3+2
5
To simplify the given complex fraction, let's break it down step by step.
The given complex fraction is:
(3 + (2 * x) / (x + 4)) ÷ (x / (x + 4))
Step 1: Simplify the numerator and denominator separately.
Numerator:
Start simplifying the numerator by distributing the multiplication:
(3 + 2x) / (x + 4)
Denominator:
The denominator is already simplified, as x divided by x+4 is x / (x + 4).
Step 2: Simplify further.
Now we have the fraction ((3 + 2x) / (x + 4)) ÷ (x / (x + 4)).
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction (flip the second fraction upside down) and then proceed to simplify.
So, the complex fraction can be rewritten as:
((3 + 2x) / (x + 4)) * ((x + 4) / x)
Step 3: Simplify the expression.
Let's simplify the numerator and denominator.
Numerator:
(3 + 2x) * (x + 4)
= 3x + 12 + 2x^2 + 8x
= 2x^2 + 11x + 12
Denominator:
(x + 4) * x
= x^2 + 4x
So, the simplified complex fraction is:
(2x^2 + 11x + 12) / (x^2 + 4x)
This is the final simplified form of the given complex fraction.