Question

посогите с номером 30, 1 пример

Answer 1

$frac{ x^{2} -9y ^{2} }{16 x^{2} -9y ^{2} }: frac{ x^{2} +6xy+9y^{2} }{16 x^{2} -24xy+9y ^{2} }= frac{ x^{2} -9y ^{2} }{16 x^{2} -9y ^{2} }cdot frac{16 x^{2} -24xy+9y ^{2} }{ x^{2} +6xy+9y^{2} }= \ =frac{(x-3y)(x+3y)}{(4x-3y)(4x+3y)}cdot frac{(4x-3y)(4x-3y)}{(x+3y)(x+3y)}=frac{(x-3y)}{(4x+3y)}cdot frac{(4x-3y)}{(x+3y)}$

Answer 2

$frac{ x^{2} -9 y^{2} }{16 x^{2} -9 y^{2} } : frac{ x^{2} +6xy+9 y^{2} }{16 x^{2} -24xy+9y ^{2} } = frac{(x-3y)(x+3y)(4x-3y)^{2}}{(4x-3y)(4x+3y)(x+3y)^{2}} = frac{(x-3y)*1*(4x-3y)}{(4x+3y)*1*(x+3y)} = \ frac{4 x^{2} -15xy+9y ^{2} }{4 x^{2} +15xy+9y^{2} }$