1) If you divide a positive (+3y) by a negative (-y), what should be the sign on the answer?
2) You have y - x, which equals -x + y, which equals -1(x - y), which then allows you to have a common denominator.
1. When factoring by grouping I am having problems understanding a particular step.
Expression:
Why are we able to change the signs towards the end of the expression? In the first step its a "-" sign and at the next step its a "+" sign.
and in the final solution the sign changes again...
2. Reducing a fraction with -1
"Reducing a fraction or adding two fractions sometimes only requires that -1 be factored from one or more denominators"
Expression:
-The book lists the steps to solve this but they are rather confusing and they do not clearly explain, I would prefer a member on here run me through the above expression and provide the how/why when solving this problem.
It's because of the parentheses.
If you take an expression like
-a - b
you can factor out a -1. In doing so, you switch the signs inside:
-1(a + b)
but you don't need to write the 1 really:
-(a + b)
Now if you have an expression like
-ax + bx
Factor out a -1x (or -x) and switch the signs inside:
-1x(a - b) = -x(a - b)
The original expression was
We're factoring by grouping. Factoring out the common factor from the first two terms is easy enough:
We factor out a -1y (or a -y) from the last two terms:
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Many Thanks Kind Sir!
Yeongil, may I also ask that you clarify my expression 2 question?
2. Reducing a fraction with -1
Expression: , now the last step here is where I become completely lost, where the denominator goes from to in the next step in solving the expression
then the last part I am also lost
in the last part of solving this expression how does the once negative denominator of go to in the next part of the solution?
I just find it easy to remember this property:
a - b = -(b - a)
So the denominator of the first fraction would be:
y - x = -(x - y)
Anyway...
You're talking about the changes in red? That's the commutative property of addition: a + b = b + a. So inside the parentheses:
-(-y + x) = -(x + (-y)) = -(x - y). You switch the x and -y.
You should also know that if you have a fraction that is negative, then the following are equivalent:in the last part of solving this expression how does the once negative denominator of go to in the next part of the solution?
We have to use this property because here:
the denominators are still not the same -- the first fraction has that negative sign outside the parenthesis. No problem -- the fraction property I stated above tells me that I can just move the negative to the numerator and the fraction is equivalent.
Hope that helps!
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