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Question 854077: Simplify the rational expression.
(9x^3-41x^2-20x) / (yx^2-2yx-15y)
Would you factor it like this?
9x^3-45x^2+4x^2-20x / yx^2+3yx-5yx-15y
Thank you for your help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! problem is:
Simplify the rational expression.
(9x^3-41x^2-20x) / (yx^2-2yx-15y)
factor out an x in the numerator to get x * (9x^2 - 41x - 20)
factor out a y in the denominator to get y * (x^2 - 2x - 15)
your expression becomes:
x * (9x^2 - 41x - 20) / (y * (x^2 - 2x - 15)
factor 9x^2 - 41x - 20 in the numerator to get x * (9x + 4) * (x - 5)
factor x^2 - 2x - 15 in the denominator to get y * (x - 5) * (x + 3)
your expression becomes:
[x * (9x + 4) * (x = 5)] / [y * (x - 5) * (x + 3)]
the (x-5) in the numerator cancels out the (x-5) in the denominator and you are left with:
(x * (9x + 4)] / [y * (x + 3)]
if you simplify this, you will get:
(9x^2 + 4x) / (yx + 3y)
that should be it.
there are many different ways to factor a quadratic.
you last resort, if you can't do it any other way, is the quadratic formula.
that formula is x = [-b +/- sqrt(b^2 - 4ac)] / 2a
once you find the roots, you then need to set the root equal to 0 in order to find the factor.
for example:
the factor of 9x + 4 creates the root of x = -4/9.
the quadratic formula will give you that root, but it will not give you the factor that created that root.
to find the factor you would do the following:
start with x = -4/9
multiply both sides of this equation by 9 to get:
9x = -4
add 4 to both sides of this equation to get 9x + 4 = 0
9x + 4 is the factor.
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