Đáp án:1a)(x+y)(x-5)
b)(2x-5)(2x+5)
c)(x+y-z)(x+y+z)
d)(x-1)(2x+5)
2)a)$\frac{x+\frac{2}{5}}{2x}$
b)$\frac{3x^{2}+5x+1}{3(x+1)(x^{2}+x+1)}$
c)$\frac{x(x-2)}{5}$
3a)x=3
b)$x=\frac{-2}{9}$
c)x=4
d)x=2
Giải thích các bước giải:
Bài 1:
a)$x(x+y) -5x-5y=x(x+y)-(5x+5y)=x(x+y)-5(x+y)=(x+y)(x-5)$
b)$4x^{2}-25=(2x)^{2}-5^{2}=(2x-5)(2x+5)$
c)$x^{2}-2xy+y^{2}-z^{2}=(x^{2}-2xy+y^{2})-z^{2}=(x+y)^{2}-z^{2}=(x+y-z)(x+y+z)$
d)$2x^{2}+3x-5=(2x^{2}-2x)+(5x-5)=2x(x-1)+5(x-1)=(x-1)(2x+5)$
Bài 2:
a)$\frac{3}{2x}+\frac{3x-3}{2x-1}+\frac{2x^{2}+1}{4x^{2}-2x}$
=$\frac{3}{2x}+\frac{3x-3}{2x-1}+\frac{2x^{2}+1}{2x(2x-1)}$
=$\frac{3(2x-1)+x(3x-3)+2x^{2}+1}{2x(2x-1)}$
=$\frac{5x^{2}-3x-2}{2x(x-1)}$
=$\frac{(x-1)(x+\frac{2}{5}}{2x(x-1)}=\frac{x+\frac{2}{5}}{2x}$
b)$\frac{3x^{2}+5x+1}{x^{3}-1}:\frac{3x+3}{x-1}$
=$\frac{3x^{2}+5x+1}{(x-1)(x^{2}+x+1}.\frac{x-1}{3(x+1)}$
=$\frac{3x^{2}+5x+1}{3(x+1)(x^{2}+x+1)}$
c)$\frac{x^{3}-8}{5x+20}·\frac{x^{2}+4x}{x^{2}+2x+4}$
=$\frac{(x-2)(x^{2}+4)}{5(x+4)}·\frac{x(x+4)}{x^{2}+2x+4}$
=$\frac{x(x-2)}{5}$
Bài 3:
a)3x + 1 =7x - 11⇔4x=12⇔ x=3
b)5-3x = 6x +7 ⇔ 9x=-2⇔ $x=\frac{-2}{9}$
c) 11-2x=x-1⇔ 3x=12⇔ x=4
d)15-8x=9-5x⇔ 3x=6⇔ x=2
