Question

Известно что 5x-15y= 1. найдите значение выражения

Answer 1

$5x-15y=1$

1) $5*x-5*3y=1$

$5*(x-3y)=1$

$5*(x-3y)= 5*\frac{1}{5}$

$x-3y= \frac{1}{5}$

2) $\frac{8}{2x-6y}=\frac{2*4}{2*x-2*3y}=\frac{2*4}{2*(x-3y)}=\frac{4}{x-3y}=$

$=\frac{4}{\frac{1}{5}}=4:\frac{1}{5}=4*\frac{5}{1}=4*5=20$

3) $\frac{18y-6x}{3}=\frac{3*6y-3*2x}{3*1}=\frac{3*(6y-2x)}{3*1}=\frac{6y-2x}{1}=6y-2x=$

$=(-2)*(-3y)+(-2)*(x)=(-2)*[(-3y)+(x)]=-2*(x-3y)=$

$=-2* \frac{1}{5}=-\frac{2}{5}$

4) $\frac{1}{x^2-6xy+9y^2}= \frac{1}{(x)^2-2*(x)*(3y)+(3y)^2}= \frac{1}{[(x)-(3y)]^2}= \frac{1}{(x-3y)^2}=$

$=\frac{1}{( \frac{1}{5} )^2}=\frac{1}{\frac{1^2}{5^2}}=\frac{1}{\frac{1}{25}}=1: \frac{1}{25}=1* \frac{25}{1} =1*25=25$