SOLUTION: Please can someone help me with this question!! thanks If x<0 and y >O Determine the sign. 1.a)xy^2 divided by y b) 1-x^2 divided by 1-y

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Question 705115: Please can someone help me with this question!! thanks
If x<0 and y >O Determine the sign.
1.a)xy^2 divided by y
b) 1-x^2 divided by 1-y

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
1a)

x < 0, so x is negative

y > 0, so y is positive

This means y^2 is positive and so is y^2 divided by y

Multiply this positive number (y^2 divided by y) with a negative number (x) to get

xy^2 over y

and this result will be negative since negative times positive = negative.

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1b)

x^2 is always positive regardless if x is positive or negative

1 - x^2 is positive only if x^2 < 1 or if -1 < x < 1

1 - y is positive only if y < 1

Since x < 0, we know for a fact that 1 - x^2 is negative (see the rule above)

Because y > 0, we know that 1-y is negative (again, look at the rule)

So 1-x^2 is negative when x < 0 and 1-y is negative when y > 0

Therefore 1-x^2 divided by 1-y is positive (negative/negative = positive)