## anonymous 4 years ago Multiplying rational expressions: x+5/4x-16 * 2x^2-32/x^2-25

1. ash2326

we have $\frac{x+5}{4x+16} * \frac{2x^2-32}{x^2-25}$ now we can take out 4 from 4x +16 and 2 from 2x^2-32 so we get $\frac{x+5}{4(x+4)} * \frac{2(x^2-16)}{x^2-25}$ now using a^-b^2=(a+b)(a-b) $\frac{x+5}{4(x+4)} * \frac{2(x+4)(x-4)}{(x-5)(x+5)}$ now we can cancel x+5 and x+4 from numerator and denominator, so we have $\frac{\cancel{x+5}}{4{\cancel{(x+4)}}} * \frac{2\cancel{(x+4)}(x-4)}{(x-5)\cancel{(x+5)}}$ so we have now $\frac{2(x-4)}{4(x-5)}$ we get finally $\frac{x-4}{2(x-5)}$

2. anonymous

why would we take oout 4 and 2?

3. anonymous

I will tell you if i said .. i give 2 apple for 4 persons then of course each person have $\frac{1}{2}$ apple its the simplest form while you said it $\frac{2}{4}, \frac{1}{2}$ both are true ... The origin of Your Qustion is simplification .. so ash2326 do that in best way .