Đáp án:

17) a. $=0$

b. $=\frac{1}{2x\left(x-1\right)}$

18) a. $=6x^3y$

b. $=\frac{30}{7yx}$

c. $=-\frac{5}{2}$

d. $-\frac{9x\left(x+y\right)}{2}$

19) a. $=\frac{2x^3}{3}$

b. $=-\frac{40}{9y^3}$

c. $=-\frac{3\left(x+y\right)}{x}$

d. $=\frac{5\left(x+1\right)}{4\left(x+3\right)}$

Giải thích các bước giải:

17) a. $\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}$

$=\frac{\left(x+3\right)\left(x-3\right)}{x\left(x-3\right)}-\frac{x^2}{x\left(x-3\right)}+\frac{9}{x\left(x-3\right)}$

$=\frac{\left(x+3\right)\left(x-3\right)-x^2+9}{x\left(x-3\right)}$

$=\frac{0}{x\left(x-3\right)}$

$=0$

b. $\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}$

$=\frac{3\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}+\frac{\left(2x-1\right)\cdot \:2x}{2x\left(x+1\right)\left(x-1\right)}-\frac{4\left(x+1\right)\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}$

$=\frac{3\left(x-1\right)+\left(2x-1\right)\cdot \:2x-4\left(x+1\right)\left(x-1\right)}{2x\left(x+1\right)\left(x-1\right)}$

$=\frac{x+1}{2x\left(x+1\right)\left(x-1\right)}$

$=\frac{1}{2x\left(x-1\right)}$

18) a. $\frac{2x^2}{y}.3xy^2$

$\frac{2x^2}{y.3xy^2}$

$=2x^2.3xy$

$=6x^2xy$

$=6x^3y$

b. $\frac{15x}{7y^3}\cdot \frac{2y^2}{x^2}$

$=\frac{15x.2y^2}{7y^3x^2}$

$=\frac{15.2y^2}{7y^3x}$

$=\frac{15.2}{7yx}$

$=\frac{30}{7yx}$

c. $\frac{5x+10}{4x-8}\cdot \frac{4-2x}{x+2}$

$=\frac{\left(5x+10\right)\left(4-2x\right)}{\left(4x-8\right)\left(x+2\right)}$

$=\frac{5\left(x+2\right)\left(4-2x\right)}{\left(4x-8\right)\left(x+2\right)}$

$=\frac{5\left(4-2x\right)}{4x-8}$

$=\frac{5.2\left(2-x\right)}{4x-8}$

$=\frac{5.2\left(2-x\right)}{4\left(x-2\right)}R$

$=\frac{5.2\left(2-x\right)}{2\cdot \:2\left(x-2\right)}$

$=\frac{5\left(2-x\right)}{2\left(x-2\right)}$

$=\frac{-5\left(x-2\right)}{2\left(x-2\right)}$

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

d. $\frac{3x^2-3y^2}{5xy}\cdot \frac{15x^2y}{2y-2x}$

$=\frac{\left(3x^2-3y^2\right).15x^2y}{5xy\left(2y-2x\right)}$

$=\frac{\left(3x^2-3y^2\right).15x^2}{5x\left(2y-2x\right)}$

$=\frac{\left(3x^2-3y^2\right).5\cdot \:3x^2}{5x\left(2y-2x\right)}$

$=\frac{\left(3x^2-3y^2\right).3x^2}{x\left(2y-2x\right)}$

$=\frac{\left(3x^2-3y^2\right).3xx}{x\left(2y-2x\right)}$

$=\frac{\left(3x^2-3y^2\right.3x}{2y-2x}$

$=\frac{3\left(x+y\right)\left(x-y\right).3x}{2y-2x}$

$=\frac{3\left(x+y\right)\left(x-y\right).3x}{2y-2x}$

$=\frac{3\left(x+y\right)\left(x-y\right).3x}{-2\left(x-y\right)}$

$=\frac{3\left(x+y\right).3x}{-2}$

$=\frac{9\left(x+y\right)x}{-2}$

$=-\frac{9\left(x+y\right)x}{2}$

$=-\frac{9x\left(x+y\right)}{2}$

19) a. $\frac{2x}{3}\div \frac{5}{5x^2}$

$=\frac{2x.5x^2}{3.5}$

$=\frac{2x^3}{3}$

b. $16x^2y^2\div \left(-\frac{18x^2y^5}{5}\right)$

$=-\frac{16x^2y^2}{\frac{18x^2y^5}{5}}$

$=-\frac{16x^2y^2.5}{18x^2y^5}$

$=-\frac{40}{9y^3}$

c. $\frac{x+y}{y-x}\div \frac{x^2+xy}{3x^2-3y^2}$

$=\frac{\left(x+y\right)\left(3x^2-3y^2\right)}{\left(y-x\right)\left(x^2+xy\right)}$

$=-\frac{\left(x+y\right).3}{x}$

$=-\frac{3\left(x+y\right)}{x}$

d. $\frac{5x-15}{4x+4}\div \frac{x^2-9}{x^2+2x+1}$

$=\frac{\left(5x-15\right)\left(x^2+2x+1\right)}{\left(4x+4\right)\left(x^2-9\right)}$

$=\frac{5\left(x+1\right)}{4\left(x+3\right)}$

Đáp án: 17) a. =0=0 b. =12x(x−1)=12x(x−1) 18) a. =6x3y=6x3y b. =307yx=307yx c. =−52=−52 d. −9x(x+y)2−9x(x+y)2 19) a. =2x33=2x33 b. =−409y3=−409y3 c. =−3(x+y)x=−3(x+y)x d. =5(x+1)4(x+3)=5(x+1)4(x+3) Giải thích các bước giải: 17) a. x+3x−xx−3+9x2−3xx+3x−xx−3+9x2−3x =(x+3)(x−3)x(x−3)−x2x(x−3)+9x(x−3)=(x+3)(x−3)x(x−3)−x2x(x−3)+9x(x−3) =(x+3)(x−3)−x2+9x(x−3)=(x+3)(x−3)−x2+9x(x−3) =0x(x−3)=0x(x−3) =0=0 b. 32x2+2x+2x−1x2−1−2x32x2+2x+2x−1x2−1−2x =3(x−1)2x(x+1)(x−1)+(2x−1)⋅2x2x(x+1)(x−1)−4(x+1)(x−1)2x(x+1)(x−1)=3(x−1)2x(x+1)(x−1)+(2x−1)⋅2x2x(x+1)(x−1)−4(x+1)(x−1)2x(x+1)(x−1) =3(x−1)+(2x−1)⋅2x−4(x+1)(x−1)2x(x+1)(x−1)=3(x−1)+(2x−1)⋅2x−4(x+1)(x−1)2x(x+1)(x−1) =x+12x(x+1)(x−1)=x+12x(x+1)(x−1) =12x(x−1)=12x(x−1) 18) a. 2x2y.3xy22x2y.3xy2 2x2y.3xy22x2y.3xy2 =2x2.3xy=2x2.3xy =6x2xy=6x2xy =6x3y=6x3y b. 15x7y3⋅2y2x215x7y3⋅2y2x2 =15x.2y27y3x2=15x.2y27y3x2 =15.2y27y3x=15.2y27y3x =15.27yx=15.27yx =307yx=307yx c. 5x+104x−8⋅4−2xx+25x+104x−8⋅4−2xx+2 =(5x+10)(4−2x)(4x−8)(x+2)=(5x+10)(4−2x)(4x−8)(x+2) =5(x+2)(4−2x)(4x−8)(x+2)=5(x+2)(4−2x)(4x−8)(x+2) =5(4−2x)4x−8=5(4−2x)4x−8 =5.2(2−x)4x−8=5.2(2−x)4x−8 =5.2(2−x)4(x−2)R=5.2(2−x)4(x−2)R =5.2(2−x)2⋅2(x−2)=5.2(2−x)2⋅2(x−2) =5(2−x)2(x−2)=5(2−x)2(x−2) =−5(x−2)2(x−2)=−5(x−2)2(x−2) =−52=−52 d. 3x2−3y25xy⋅15x2y2y−2x3x2−3y25xy⋅15x2y2y−2x =(3x2−3y2).15x2y5xy(2y−2x)=(3x2−3y2).15x2y5xy(2y−2x) =(3x2−3y2).15x25x(2y−2x)=(3x2−3y2).15x25x(2y−2x) =(3x2−3y2).5⋅3x25x(2y−2x)=(3x2−3y2).5⋅3x25x(2y−2x) =(3x2−3y2).3x2x(2y−2x)=(3x2−3y2).3x2x(2y−2x) =(3x2−3y2).3xxx(2y−2x)=(3x2−3y2).3xxx(2y−2x) =(3x2−3y23x2y−2x=(3x2−3y23x2y−2x =3(x+y)(x−y).3x2y−2x=3(x+y)(x−y).3x2y−2x =3(x+y)(x−y).3x2y−2x=3(x+y)(x−y).3x2y−2x =3(x+y)(x−y).3x−2(x−y)=3(x+y)(x−y).3x−2(x−y) =3(x+y).3x−2=3(x+y).3x−2 =9(x+y)x−2=9(x+y)x−2 =−9(x+y)x2=−9(x+y)x2 =−9x(x+y)2=−9x(x+y)2 19) a. 2x3÷55x22x3÷55x2 =2x.5x23.5=2x.5x23.5 =2x33=2x33 b. 16x2y2÷(−18x2y55)16x2y2÷(−18x2y55) =−16x2y218x2y55=−16x2y218x2y55 =−16x2y2.518x2y5=−16x2y2.518x2y5 =−409y3=−409y3 c. x+yy−x÷x2+xy3x2−3y2x+yy−x÷x2+xy3x2−3y2 =(x+y)(3x2−3y2)(y−x)(x2+xy)=(x+y)(3x2−3y2)(y−x)(x2+xy) =−(x+y).3x=−(x+y).3x =−3(x+y)x=−3(x+y)x d. 5x−154x+4÷x2−9x2+2x+15x−154x+4÷x2−9x2+2x+1 =(5x−15)(x2+2x+1)(4x+4)(x2−9)=(5x−15)(x2+2x+1)(4x+4)(x2−9) =5(x+1)4(x+3)