Answer:
Step-by-step explanation:
a² - b² = (a+ b)(a - b)
1) (2n-4/2n) ÷ (n^2-4/n)
[tex]=\frac{2n-4}{2n}*\frac{n}{n^{2}-4}\\\\=\frac{2n-2*2}{2n}*\frac{n}{n^{2}-2^{2}}\\\\=\frac{2*(n-2)}{2n}*\frac{n}{(n+2)*(n-2)}\\\\=\frac{1}{n+2}[/tex]
2) [y^2-36/y^2-49] ÷[ y+6/y-7]
[tex]=\frac{y^{2}-36}{y^{2}-49}*\frac{y-7}{y+6}\\\\=\frac{y^{2}-6^{2}}{y^{2}-7^{2}}*\frac{y-7}{y+6}\\\\=\frac{(y+6)*(y-6)}{(y+7)*(y-7)}*\frac{y-7}{y+6}\\\\=\frac{y-6}{y+7}\\[/tex]
3) [m^2-1/ m^2-m] ÷ [m^2-7m-8/3m
]
[tex]=\frac{m^{2}-1}{m^{2}-m}*\frac{3m}{m^{2}-7m-8}\\\\=\frac{(m+1)*(m-1)}{m*(m-1)}*\frac{3m}{(m-8)*(m+1)}\\\\=\frac{3}{m-8}[/tex]
Hint : m² - 7m - 8
sum = -7
Product = -8
Factor = (-8), 1
m² - 7m - 8 =m² - 8m + m - 8
= m*(m - 8) + (m-8)
= (m - 8)(m +1)
