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

Guest Oct 4, 2017
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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. $$\frac{4x^2-14x+6}{3x^2+4x-15}$$
TheXSquaredFactor  Oct 4, 2017

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