Assuming that x doesn't equal to -3 simplify ((8x-4)/(x+3))/((12x-20)/(2x-6))
+2446 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. |
| \(\frac{4x^2-14x+6}{3x^2+4x-15}\) |
