How do you simplify #(15x^2-8x-18)/(-20x^2+14x+12)#?

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Answer 1 · 2016-09-30T20:30:38

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The only way to simplify a rational polynomial expression is to group something, usualy by finding the solutions, or any other factoring technique.

For example, we can factor a #2# in the denominator, so that it becomes

#2(-10x^2+7x+6)#.

As for the solutions, the denominator looks pretty ugly: we have

#15x^2-8x-18 = 0 \iff x = 4/15 \pm sqrt(286)/15#

The denominator is much easier:

#-10x^2+7x+6 = 0 \iff x=-1/2# or #6/5#

This means that we can write our fraction as

#((x-4/15-sqrt(286)/15)(x-4/15+sqrt(286)/15))/(2(-2x+1)(5x-6))#

And there's nothing we can simplify.

As you can see here WolframAlpha can only group something in the numerator or denominator, but can't cancel anything that is present in both.