Assuming that x doesn't equal to -3 simplify ((8x-4)/(x+3))/((12x-20)/(2x-6))

 Oct 4, 2017

To simplify this monstrosity \(\frac{\frac{8x-4}{x+3}}{\frac{12x-20}{2x-6}}\), we must eliminate the inner fractions.


\(\frac{\frac{8x-4}{x+3}}{\frac{12x-20}{2x-6}}*\frac{\frac{2x-6}{12x-20}}{\frac{2x-6}{12x-20}}\) Multiply by the reciprocal of the denominator to eliminate the fraction in a fraction. This may look complicated, but we are actually multiplying the fraction by 1, which does not affect its value. 
\(\frac{8x-4}{x+3}*\frac{2x-6}{12x-20}\) Now, multiply the fractions together. Let's start with the numerator.
\((8x-4)(2x-6)=16x^2-48x-8x+24=16x^2-56x+24\) Do the same with the denominator.
\((x+3)(12x-20)=12x^2-20x+36x-60=12x^2+16x-60\) Now, combine them together.
\(\frac{16x^2-56x+24}{12x^2+16x-60}\) Both the numerator and denominator both have a GCF of 4.
 Oct 4, 2017

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