Reduce the rational expression to lowest terms.
250y+100xy+10x^2y/125y−5x^2y
(i really need to know the steps on how to do this (please just don't give me the answer i already know it)
YOu have to factor both the top and bottom of the rational expression. YOu must state restrictions on both variables (using the factored form of the denominator : )
To reduce the rational expression to lowest terms, you need to simplify both the numerator and the denominator as much as possible. Let's start by factoring out common terms.
Numerator (250y + 100xy + 10x^2y):
= 10y(25 + 10x + x^2)
Denominator (125y - 5x^2y):
= 5y(25 - x^2)
Now, you can cancel out any common factors between the numerator and the denominator.
Cancelling out a common factor of 5y, we get:
= 2(25 + 10x + x^2) / (25 - x^2)
Next, let's try to further simplify this expression by factoring the numerator and denominator completely.
Numerator (25 + 10x + x^2):
= (5 + x)^2
Denominator (25 - x^2):
= (5 - x)(5 + x)
Now, you can cancel out common factors again:
= 2(5 + x)^2 / (5 - x)(5 + x)
Finally, we can cancel out the common factor of (5 + x):
= 2(5 + x) / (5 - x)
So, the rational expression 250y+100xy+10x^2y / 125y−5x^2y reduces to 2(5 + x) / (5 - x) in its lowest terms.