Eliminate the complex fractions
(5/8)/(-2/3)
(x^-1+y^-1)/(x+y)
(1/x+1/y)/(x+y) (xy/xy/)
I was trying to find the lcd for the first one but couldn't figure it out. For the second one, I got to as far as getting the reciprocal of the numerator and then multiplying by xy but I wasn't sure if that was right.
(5/8)/(-2/3)
= (5/8)(-3/2)
= -15/16
(x^-1+y^-1)/(x+y)
= (1/x + 1/y)/(x+y)
= ((x+y)/(xy))/(x+y)
= 1/(xy)
So the first one, all I had to do was divide it normally? Do I do that if there are no lcd's for problems like that?
you only need an lcd if you are adding fractions with unlike denominators.
Multiplication and division just work on the tops and bottoms separately.
THANK YOUU
To eliminate complex fractions, you need to simplify them by getting rid of the fractional parts within the numerator and denominator.
1. (5/8)/(-2/3):
To eliminate the complex fraction, you can multiply the numerator by the reciprocal of the denominator. In this case, you would multiply (5/8) by (3/-2). This gives you [(5/8) * (3/-2)] = (-15/16).
2. (x^-1+y^-1)/(x+y):
To eliminate the complex fraction, you can follow these steps:
- Expand the expression to get [(1/x + 1/y)]/(x + y).
- Find the LCD (Least Common Denominator) for the fractions in the numerator. The LCD in this case is xy.
- Multiply the numerator and denominator by the LCD to eliminate the complex fraction. This gives you [(1/x)*(xy) + (1/y)*(xy)] / [(x + y)*(xy)].
- Simplify the expression to get (y + x)/(x*y*(x + y)).
Please note that it seems like you made a mistake while simplifying the second expression. The reciprocal of the numerator in the second expression should be (1/(x + y)) rather than (x + y).