How do you subtract 2xx2+10x+25−3x2x2+7x−15?

1 Answer
Nico Ekkart
Dec 20, 2014

First, we're going to simplify the expressions a bit. We can do this by factoring both the denominators:
x2+10x+25=(x+5)2

2x2+7x−15=(x+5)(2x−3)

To substract two fractions with a different denominator, we will always have to find the LCM of the denominators. In this case it is (x+5)2(2x−3) since this can evenly be divided by both the denominators.

Let's combine what we've got already:
2x(x+5)2−3x(x+5)(2x−3)

Now for changing to the LCM:
2x−32x−3⋅2x(x+5)2−x+5x+53x(x+5)(2x−3)

=2x⋅(2x−3)−3x⋅(x+5)(x+5)2(2x−3)

Distribute the terms:

4x2−6x−3x2−15x(x+5)2(2x−3)

=x2−21x(x+5)2(2x−3)

You could've also done this without factoring, but it would've been way harder. Factoring always makes your life easier!

I really hope this helped.

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