Ok one last complex fraction on the worksheet, can i get some help with it?
[(x/3)-4]
---------
[5+(1/x)]
multiply numerator and denominator by 3x
result:
( x^2 - 12x)/(15x + 3)
Ok ive attempted what i think might be an answer...
x-12
----
3
----
5x+1
----
x
Right?
and then i flip flopped it so i could multiply it..
(x-12) x
------ x -----
3 5x+1
(the x in the middle symbolizes multiplication)
so after i multiply them out i get...
(x^2)-12x
---------
15x +3
so is that the right answer?
SOLID! thanks reiny!
Of course! I'd be happy to help you with the complex fraction. To simplify the given expression, we can follow these steps:
Step 1: Find a common denominator for the fraction in the numerator and the fraction in the denominator. In this case, the common denominator is 3x.
Step 2: Rewrite the complex fraction using the common denominator.
[(x/3)-4] / [5+(1/x)] can be written as:
[(x/3) * (x/x) - 4*(x/3x)] / [(5x/x) + (1/x)]
Simplifying further, we get:
[(x^2/3x) - (4x/3x)] / [(5x/x) + (1/x)]
Step 3: Combine like terms in the numerator and denominator.
[(x^2 - 4x) / 3x] / [(5x + 1) / x]
Step 4: Divide by a fraction by multiplying with the reciprocal.
[(x^2 - 4x) / 3x] * [x / (5x + 1)]
Step 5: Simplify the expression.
(x^2 - 4x) / (3x) * (x / (5x + 1))
Finally, we have simplified the complex fraction [(x/3) - 4] / [5 + (1/x)] to (x^2 - 4x) / (3x) * (x / (5x + 1)).