Question

1)3a^2-6ab+3b^2/6a^2-6b^2 2)5m^2+10mn+5n^2/15m^2-15n^2

Answer 1

1) $frac{3a^{2}-6ab+3b^{2}}{6a^{2}-6b^{2}}=frac{3(a^{2}-2ab+b^{2})}{6(a^{2}-b^{2})}=frac{(a-b)(a-b)}{2((a-b)(a+b))}=frac{a-b}{2(a+b)}=frac{a-b}{2a+2b}$

 

 

2) $frac{5m^{2}+10mn+5n^{2}}{15m^{2}-15n^{2}}=frac{5(m^{2}+2mn+n^{2})}{15(m^{2}-n^{2})}=frac{(m+n)(m+n)}{3((m-n)(m+n))}=frac{m+n}{3(m-n)}=frac{m+n}{3m-3n}$