1. 2 Упростите выражение

Question 1

1. $(\frac{3}{x-4}+\frac{4x-6}{x^2-3x-4}+\frac{2x}{x+1})*\frac{x}{2x-3}$

2 $(\frac{2}{2-x}+\frac{3x-21}{x^2+x-6}+\frac{2x}{x+3})*\frac{x}{2x-5}$

Упростите выражение

Question 2

решение в прикреплённом файле

Question 3

№ 1

$(\frac{3}{x-4}+\frac{4x-6}{x^2-3x-4}+\frac{2x}{x+1})\cdot\frac{x}{2x-3}=\frac{x}{x-4}$

1) $\frac{3}{x-4}+\frac{4x-6}{x^2-3x-4}=\frac{3}{x-4}+\frac{4x-6}{(x-4)(x+1)}=\frac{3(x+1)+4x-6}{(x-4)(x+1)}=\frac{3x+3+4x-6}{(x-4)(x+1)}=\frac{(3x+4x)+(3-6)}{(x-4)(x+1)}=\frac{7x-3}{(x-4)(x+1)}$

2) $\frac{7x-3}{(x-4)(x+1)}+\frac{2x}{x+1}=\frac{7x-3+2x(x-4)}{(x-4)(x+1)}=\frac{7x-3+2x^{2}-8x}{(x-4)(x+1)}=\frac{2x^{2}+(7x-8x)-3}{(x-4)(x+1)}=\frac{2x^{2}-x-3}{(x-4)(x+1)}$ = $\frac{2(x+1)(x-1,5)}{(x-4)(x+1)}=\frac{2(x-1,5)}{x-4}=\frac{2x-3}{x-4}$

3) $\frac{2x-3}{x-4}\cdot\frac{x}{2x-3}=\frac{x(2x-3)}{(x-4)(2x-3)}=\frac{x}{x-4}$

№ 2

$(\frac{2}{2-x}+\frac{3x-21}{x^2+x-6}+\frac{2x}{x+3})\cdot\frac{x}{2x-5}=\frac{x^{2}-4,5x}{x^{2}-4,5x-5}$

1) $\frac{2}{2-x}+\frac{3x-21}{x^2+x-6}=\frac{2}{2-x}+\frac{3x-21}{(x+3)(x-2)}=\frac{2}{-x+2}+\frac{3x-21}{(x+3)(x-2)}=\frac{2}{-(x-2)}+\frac{3x-21}{(x+3)(x-2)}=-\frac{2}{x-2}+\frac{3x-21}{(x+3)(x-2)}$ = $\frac{3x-21}{(x+3)(x-2)}-\frac{2}{x-2}=\frac{3x-21-2(x+3)}{(x+3)(x-2)}=\frac{3x-21-2x-6}{(x+3)(x-2)}=\frac{(3x-2x)+(-21-6)}{(x+3)(x-2)}=\frac{x-27}{(x+3)(x-2)}$

2) $\frac{x-27}{(x+3)(x-2)}+\frac{2x}{x+3}=\frac{x-27+2x(x-2)}{(x+3)(x-2)}=\frac{x-27+2x^{2}-4x}{(x+3)(x-2)}=\frac{2x^{2}+(x-4x)-27}{(x+3)(x-2)}=\frac{2x^{2}-3x-27}{(x+3)(x-2)}=$ = $\frac{2(x+3)(x-4,5)}{(x+3)(x-2)}=\frac{2(x-4,5)}{x-2}=\frac{2x-9}{x-2}$

3) $\frac{2x-9}{x-2}\cdot\frac{x}{2x-5}=\frac{2(x-4,5)}{x-2}\cdot\frac{x}{2(x-2,5)}= \frac{2x(x-4,5)}{2(x-2,5)(x-2)}=\frac{x(x-4,5)}{(x-2,5)(x-2)}=\frac{x^{2}-4,5x}{x^{2}-2x-2,5x-5}=$ = $\frac{x^{2}-4,5x}{x^{2}-4,5x-5}$