[tex]\displaystyle\bf\\\frac{25x^{2} -30xy+9y^{2} }{25x^{2} -9y^{2} }=\frac{(5x)^{2} -2\cdot 5x\cdot 3y+(3y)^{2} }{(5x)^{2}-(3y)^{2} } =\\\\\\=\frac{(5x-3y)^{2} }{(5x-3y)(5x+3y)}=\frac{5x-3y}{5x+3y}[/tex]

При решении были применены формулы :

[tex]\displaystyle\bf\\1) \ a^{2}-2ab+b^{2} =(a-b)^{2} \\\\\\2) \ a^{2} -b^{2} =(a-b)(a+b)[/tex]