SOLUTION: Please help, this is a complex fraction 12x + 16 + 5/x over 18x - 27 - 35/x Do I use x as a LCD, ?? 12x^2 + 16x + 5 over 18x^2 -27x -35 or would the x's cancel on the 12

Question 73191: Please help, this is a complex fraction
12x + 16 + 5/x
over
18x - 27 - 35/x
Do I use x as a LCD, ?? 12x^2 + 16x + 5 over 18x^2 -27x -35 or would the x's cancel on the 12 and 18???????????? Please walk me through.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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You can use x as an LCD in both the numerator and denominator, but it may be quicker for
you to just multiply the fraction (both numerator and denominator) by x. In effect this is
multiplying the fraction of the problem by which will not change the result of the
division because it is the same as multiplying the fraction by 1.
.
Multiplying the numerator by x (all three terms are multiplied by x) results in changing
the numerator to:
.

.
Similarly, multiplying all three terms of the denominator by x changes the denominator
to:
.

.
so the problem is now modified to:
.

.
The numerator factors to and the denominator factors to
so the problem becomes:
.

.
and canceling the common factor in the numerator and denominator:
.

.
reduces the problem to:
.

.
and that is the answer.
.
Hope this provides a little easier way of looking at how to work the problem. It is
just a little more convenient than using the LCD, but the LCD method would work.

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