Question

ПЖАЖПЖАЖАЖАЖ ДПМ КУЧУ БАЛОВ​

Answer 1

1.

1)

$\frac{8m-5n}{mn}-\frac{2m-5n}{mn} =\frac{8m-5n-2m+5n}{mn} =\frac{6m}{mn} =\frac{6}{n}$

2)

$\frac{2y}{y^{2}-49} -\frac{14}{y^{2}-49} =\frac{2y-14}{(y-7)(y+7)} =\frac{2(y-7)}{(y-7)(y+7)} =\frac{2}{y+7}$

3)

$\frac{x^{2}+12x}{25-x^{2}} -\frac{2x-25}{25-x^{2}} =\frac{x^{2}+12x-2x+25}{(5-x)(5+x)} =\frac{x^{2}+10x+25}{(5-x)(5+x)} =\frac{(x+5)^{2}}{(5-x)(5+x)} =\frac{x+5}{5-x}$

2.

1)

$\frac{x^{3}-7}{1-x} -\frac{6}{x-1} =\frac{x^{3}-7}{1-x} +\frac{6}{1-x} =\frac{x^{3}-7+6}{1-x} =\frac{x^{3}-1}{1-x} =-\frac{(x-1)(x^{2}+x+1)}{x-1} =-(x^{2}+x+1)=\\\\=-x^{2}-x-1$

2)

$\frac{36-8x}{(x-6)^{2}} -\frac{4x-x^{2}}{(6-x)^{2}} =\frac{36-8x}{(x-6)^{2}}-\frac{4x-x^{2}}{(-(x-6))^{2}} =\frac{36-8x}{(x-6)^{2}}-\frac{4x-x^{2}}{(x-6)^{2}} =\frac{36-8x-4x+x^{2}}{(x-6)^{2}} =\\\\=\frac{x^{2}-12x+36}{(x-6)^{2}} =\frac{(x-6)^{2}}{(x-6)^{2}} =1$