Question

9x²-4y²/20y²-60xy+45x² =при x=2/3 y= 0,75

Answer 1

$\frac{9 x^{2} -4 y^{2} }{20 y^{2}-60xy+45 x^{2} } = \frac{(3x-2y)(3x+2y)}{5(4 y^{2} -12xy+9 x^{2}) } =\frac{(3x-2y)(3x+2y)}{5(9 x^{2} -12xy+4y ^{2} ) } =$

$=\frac{(3x-2y)(3x+2y)}{5(3x-2y ) ^{2} } = \frac{3x+2y}{5(3x-2y)}$

При $x= \frac{2}{3}$ , y = 0,75  
 $\frac{3x+2y}{5(3x-2y)} = \frac{3* \frac{2}{3} +2*0,75}{5(3* \frac{2}{3}-2*0,75) } = \frac{2+1,5}{5*(2-1,5)} \= \frac{3,5}{5*0,5} =$$=\frac{3,5}{2,5} = 1,4$