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.

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