Question

помогите пожалуйста. ​

Answer 1

$1)\frac{t^{2}-4t+16 }{16t^{2}-1 }*\frac{4t^{2}+t }{t^{3}+64 }-\frac{t+4}{4t^{2}-t }=\frac{(t^{2}-4t+16)*t*(4t+1)}{(4t-1)(4t+1)(t+4)(t^{2}-4t+16)}-\frac{t+4}{t(4t-1)}=\\\\=\frac{t}{(4t-1)(t+4)}-\frac{t+4}{t(4t-1)}=\frac{t^{2}-(t+4)^{2}}{t(4t-1)(t+4)}=\frac{t^{2}-t^{2} -8t-16}{t(4t-1)(t+4)}=\frac{-8(t+2)}{t(4t-1)(t+4)}$

$2)\frac{-8(t+2)}{t(4t-1)(t+4)} :\frac{4}{t^{2}+4t } =\frac{-8(t+2)}{t(4t-1)(t+4)}*\frac{t(t+4)}{4}=\frac{-2(t+2)}{4t-1}\\\\\\3)\frac{-2(t+2)}{4t-1}-\frac{20t+13}{4-16t}=\frac{-2t-4}{4t-1} -\frac{20t+13}{4(1-4t)}=\frac{-2t-4}{4t-1} +\frac{20t+13}{4(4t-1)} =\\\\=\frac{-8t-16+20t+13}{4(4t-1)} =\frac{12t-3}{4(4t-1)}=\frac{3(4t-1)}{4(4t-1)} =\boxed{\frac{3}{4}}$