How do i simplify this complex fraction?
(x+3)/(3x^2)/(6x^2)/[(x+3)^2]
according to the order of operation,
in a chain of division, you divide from left to right, in the order in which the division occurs.
e.g.
13÷2÷6÷4 = .25
or
= 12*(1/2)*(1/6)*(1/4) = .25
so How do i simplify this complex fraction?
(x+3)/(3x^2)/(6x^2)/[(x+3)^2]
= (x+3) (1/(3x^2)(1/6x^2)(1/(x+3)^2
= 1/(18x^4(x+3))
Isn't there a different method you're sposed to use? like finding a common denominator? im thankful that your helping me but all those number got a little confusing... what if i said it looked more like this
the dash mark is a division symbol... this is what it looks like on my paper.
x+3
-----
3x^2
------
6x^2
------
(x+3)^2
You don't need common denominators in division or multiplication.
If the fraction is written as a staggered layer of expressions, the division bar should have different length to establish the order of division.
If all the bars are the same length, then the simplification I used above is valid
In other words, the longest bar determines the prime division.
To simplify the given complex fraction, follow these steps:
Step 1: Flip the numerator and denominator of the complex fraction that is inside the main fraction, i.e.,
(x+3)/(3x^2)/(6x^2)/[(x+3)^2] = (x+3)/(3x^2) * [(x+3)^2]/(6x^2)
Step 2: Multiply the terms in the numerator and denominator that involve variables. In this case, we have (x+3) in the numerator and [(x+3)^2] in the denominator, so let's simplify this part first:
(x+3)/(3x^2) * [(x+3)^2]/(6x^2) = (x+3)/(3x^2) * (x+3)(x+3)/(6x^2)
Step 3: Simplify the numerator by multiplying the terms using the distributive property:
(x+3) * (x+3) = x * (x+3) + 3 * (x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9
Step 4: Simplify the denominator by multiplying the terms using the distributive property:
(6x^2) * (x^2) = 6x^4
Step 5: Substitute the simplified numerator and denominator back into the main fraction:
(x+3)/(3x^2) * [(x+3)^2]/(6x^2) = (x^2 + 6x + 9)/(3x^2 * 6x^2)
Step 6: Combine like terms in the numerator and simplify the denominator:
(x^2 + 6x + 9)/(3x^2 * 6x^2) = (x^2 + 6x + 9)/(18x^4)
Step 7: Factor the numerator, if possible:
(x^2 + 6x + 9) = (x+3)(x+3) = (x+3)^2
Step 8: Substitute the factored numerator back into the simplified fraction:
(x+3)^2/(18x^4)
Therefore, the simplification of the given complex fraction is (x+3)^2/(18x^4).