Mathematics

HELP!!!!  multiply and simplify  r⁴-16/r⁴-81·r²+9/r²+4 simplified product is ______

Quan336

4 years ago

$\frac{ r^{4} -16}{ r^{4} -81}* \frac{ r^{2}+9 }{ r^{2}+4 }$

ok the best way to look at this is by factoring out so look at "r^4-16" if you factor out you get (r²-4)(r²+4) and the same with "r^4-81" if you factor out you get (r²-9)(r²+9)

so now your problem looks something like this.
$\frac{( r^{2} -4)( r^{2} +4)( r^{2} +9)}{( r^{2} -9)( r^{2} +9)( r^{2} +4)}$

now cancel out like terms remember  $\frac{ab}{bc}= \frac{a}{c}$ because b/b=1

so now your left with $\frac{( r^{2} -4)}{ r^{2} -9}$

lisaacervante

4 years ago

Well, even this expression given by 'secretlyblu' can be factorized:
$\frac{r^2-4}{r^2-9} = \frac{(r+2)(r-2)}{(r+3)(r-3)}$