Rút gọn các phân thức sau:
1. (x2+2)2−4x2y(x2+2)−2xy−(x−1)2−1\dfrac{\left(x^2+2\right)^2-4x^2}{y\left(x^2+2\right)-2xy-\left(x-1\right)^2-1}y(x2+2)−2xy−(x−1)2−1(x2+2)2−4x2
2. x2+5x+6x2+3x+2\dfrac{x^2+5x+6}{x^2+3x+2}x2+3x+2x2+5x+6
3. x2+y2−z2−2zt+2xy−t2x2−y2+z2−2zt+2xz−t2\dfrac{x^2+y^2-z^2-2zt+2xy-t^2}{x^2-y^2+z^2-2zt+2xz-t^2}x2−y2+z2−2zt+2xz−t2x2+y2−z2−2zt+2xy−t2
4. (n+1)!(n+1)!+(n+2)!\dfrac{\left(n+1\right)!}{\left(n+1\right)!+\left(n+2\right)!}(n+1)!+(n+2)!(n+1)!
5. x2+5x+4x2−1\dfrac{x^2+5x+4}{x^2-1}x2−1x2+5x+4
6. x2−3x2x2−7x+3\dfrac{x^2-3x}{2x^2-7x+3}2x2−7x+3x2−3x
1. (x2+2)2−4x2y(x2+2)−2xy−(x−1)2−1=(x2+2−2x)(x2+2+2x)x2y+2y−2xy−x2+2x−1−1=(x2+2−2x)(x2+2+2x)(x2y−x2)−(2xy−2x)+(2y−2)=(x2+2−2x)(x2+2+2x)x2(y−1)−2x(y−1)+2(y−1)=(x2+2−2x)(x2+2+2x)(x2−2x+2)(y−1)=x2+2x+2y−11.\text{ }\text{ }\text{ }\dfrac{\left(x^2+2\right)^2-4x^2}{y\left(x^2+2\right)-2xy-\left(x-1\right)^2-1}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{x^2y+2y-2xy-x^2+2x-1-1}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{\left(x^2y-x^2\right)-\left(2xy-2x\right)+\left(2y-2\right)}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{x^2\left(y-1\right)-2x\left(y-1\right)+2\left(y-1\right)}\\ =\dfrac{\left(x^2+2-2x\right)\left(x^2+2+2x\right)}{\left(x^2-2x+2\right)\left(y-1\right)}\\ =\dfrac{x^2+2x+2}{y-1}1. y(x2+2)−2xy−(x−1)2−1(x2+2)2−4x2=x2y+2y−2xy−x2+2x−1−1(x2+2−2x)(x2+2+2x)=(x2y−x2)−(2xy−2x)+(2y−2)(x2+2−2x)(x2+2+2x)=x2(y−1)−2x(y−1)+2(y−1)(x2+2−2x)(x2+2+2x)=(x2−2x+2)(y−1)(x2+2−2x)(x2+2+2x)=y−1x2+2x+2
2. x2+5x+6x2+3x+2=x2+3x+2x+6x2+2x+x+2=(x2+3x)+(2x+6)(x2+2x)+(x+2)=x(x+3)+2(x+3)x(x+2)+(x+2)=(x+2)(x+3)(x+2)(x+1)=x+3x+12.\text{ }\text{ }\text{ }\text{ }\dfrac{x^2+5x+6}{x^2+3x+2}\\ =\dfrac{x^2+3x+2x+6}{x^2+2x+x+2}\\ =\dfrac{\left(x^2+3x\right)+\left(2x+6\right)}{\left(x^2+2x\right)+\left(x+2\right)}\\ =\dfrac{x\left(x+3\right)+2\left(x+3\right)}{x\left(x+2\right)+\left(x+2\right)}\\ =\dfrac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+1\right)}\\ =\dfrac{x+3}{x+1}2. x2+3x+2x2+5x+6=x2+2x+x+2x2+3x+2x+6=(x2+2x)+(x+2)(x2+3x)+(2x+6)=x(x+2)+(x+2)x(x+3)+2(x+3)=(x+2)(x+1)(x+2)(x+3)=x+1x+3
3. x2+y2−z2−2zt+2xy−t2x2−y2+z2−2yt+2xz−t2 ( Chữa đeˆˋ ) =(x2+2xy+y2)−(z2+2zt+t2)(x2+2xz+z2)−(y2+2yt+t2)=(x+y)2−(z+t)2(x+z)2−(y+t)2=(x+y+z+t)(x+y−z−t)(x+z+y+t)(x+z−y−t)=x+y−z−tx+z−y−t3.\text{ }\text{ }\text{ }\dfrac{x^2+y^2-z^2-2zt+2xy-t^2}{x^2-y^2+z^2-2yt+2xz-t^2}\text{ ( Chữa đề ) }\\ =\dfrac{\left(x^2+2xy+y^2\right)-\left(z^2+2zt+t^2\right)}{\left(x^2+2xz+z^2\right)-\left(y^2+2yt+t^2\right)}\\ =\dfrac{\left(x+y\right)^2-\left(z+t\right)^2}{\left(x+z\right)^2-\left(y+t\right)^2}\\ =\dfrac{\left(x+y+z+t\right)\left(x+y-z-t\right)}{\left(x+z+y+t\right)\left(x+z-y-t\right)}\\ =\dfrac{x+y-z-t}{x+z-y-t}3. x2−y2+z2−2yt+2xz−t2x2+y2−z2−2zt+2xy−t2 ( Chữa đeˆˋ ) =(x2+2xz+z2)−(y2+2yt+t2)(x2+2xy+y2)−(z2+2zt+t2)=(x+z)2−(y+t)2(x+y)2−(z+t)2=(x+z+y+t)(x+z−y−t)(x+y+z+t)(x+y−z−t)=x+z−y−tx+y−z−t
4. (n+1)!(n+1)!+(n+2)!=(n+1)!(n+1)!(1+n+2)=1n+34.\text{ }\text{ }\text{ }\dfrac{\left(n+1\right)!}{\left(n+1\right)!+\left(n+2\right)!}=\dfrac{\left(n+1\right)!}{\left(n+1\right)!\left(1+n+2\right)}=\dfrac{1}{n+3}4. (n+1)!+(n+2)!(n+1)!=(n+1)!(1+n+2)(n+1)!=n+31
5. x2+5x+4x2−1=x2+x+4x+4(x+1)(x−1)=(x2+x)+(4x+4)(x+1)(x−1)=x(x+1)+4(x+1)(x+1)(x−1)=(x+1)(x+4)(x+1)(x−1)=x+4x−15.\text{ }\text{ }\text{ }\dfrac{x^2+5x+4}{x^2-1}\\ =\dfrac{x^2+x+4x+4}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{\left(x^2+x\right)+\left(4x+4\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{x\left(x+1\right)+4\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{\left(x+1\right)\left(x+4\right)}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{x+4}{x-1}5. x2−1x2+5x+4=(x+1)(x−1)x2+x+4x+4=(x+1)(x−1)(x2+x)+(4x+4)=(x+1)(x−1)x(x+1)+4(x+1)=(x+1)(x−1)(x+1)(x+4)=x−1x+4
6. x2−3x2x2−7x+3=x(x−3)2x2−6x−x+3=x(x−3)(2x2−6x)−(x−3)=x(x−3)2x(x−3)−(x−3)=x(x−3)(2x−1)(x−3)=x2x−16.\text{ }\text{ }\text{ }\dfrac{x^2-3x}{2x^2-7x+3}\\ =\dfrac{x\left(x-3\right)}{2x^2-6x-x+3}\\ =\dfrac{x\left(x-3\right)}{\left(2x^2-6x\right)-\left(x-3\right)}\\ =\dfrac{x\left(x-3\right)}{2x\left(x-3\right)-\left(x-3\right)}\\ =\dfrac{x\left(x-3\right)}{\left(2x-1\right)\left(x-3\right)}\\ =\dfrac{x}{2x-1}6. 2x2−7x+3x2−3x=2x2−6x−x+3x(x−3)=(2x2−6x)−(x−3)x(x−3)=2x(x−3)−(x−3)x(x−3)=(2x−1)(x−3)x(x−3)=2x−1x
Tìm giá trị lớn nhất hoặc nhỏ nhất
2−4x2+8x−5\dfrac{2}{-4x^2+8x-5}−4x2+8x−52
4x2+8x−54x^2+8x-54x2+8x−5
Giúp mình với nhé !
1) A= 6x/x^2-9 - 5x/3-x + x/ x+3
4x2−4x−1>04x^2-4x-1>04x2−4x−1>0
Quy đồng mẫu thức các phân thức:
a,3x2x+4\dfrac{3x}{2x+4}2x+43xvà x+3x2−4\dfrac{x+3}{x^2-4}x2−4x+3
a,5x5y3\dfrac{5}{x^5y^3}x5y35,712x3y4\dfrac{7}{12x^3y^4}12x3y47
quy đồng mẫu thức hai phân thức sau
x+5x2+4x+4vaˋx3x+6\dfrac{x+5}{x^2+4x+4}và\dfrac{x}{3x+6}x2+4x+4x+5vaˋ3x+6x
Quy đồng mẫu các phân thức: 1) 7x-1/2x^2+6x; 3-2x/x^2-9 2) 2x-1/x-x^2; x+1/2-4x+2x^2 3) x-1/x^3+1; 2x/x^2-x+1; 2/x+1 4) 7/5x; 4/x-2y; x-y/8y^2-2x^2 5) x/x^3-1; x+1/x^2-x; x-1/x^2+x+1 6) x/x^2-2ax+a^2; x+a/x^2-ax
QUy đồng
5x2x2+5x+6;2x+3x2+7x+10;−5\dfrac{5x^2}{x^2+5x+6};\dfrac{2x+3}{x^2+7x+10};-5x2+5x+65x2;x2+7x+102x+3;−5
Cho các phân thức:
1x−2;152x−1;x−5x−2\dfrac{1}{x-2};\dfrac{15}{2x-1};\dfrac{x-5}{x-2}x−21;2x−115;x−2x−5
a) Tìm x nguyên để các phân thức đó có giá trị nguyên
b) Quy đồng mẫu thức các phân thức đó
