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Bài 1:
a) \(\dfrac{15xy}{10x^2y}\)
= \(\dfrac{3.5xy}{2.5xyx}\)
= \(\dfrac{3}{2x}\)
d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)
= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)
= \(\dfrac{3\left(x+5\right)^2}{x}\)
1)
a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)
b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)
c) \(\dfrac{21x^2y^3}{6xy}=\dfrac{7xy^2}{2}\left(xy\ne0\right)\)
d) \(\dfrac{2x+2y}{4}=\dfrac{2\left(x+y\right)}{4}=\dfrac{x+y}{2}\)
e) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5\left(x-y\right)}{3\left(x-y\right)}=\dfrac{5}{3}\left(x\ne y\right)\)
f) \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}=-5x\dfrac{x-y}{y-x}=-5x\dfrac{x-y}{-\left(x-y\right)}\)
\(=-5x.\left(-1\right)=5x\left(x\ne y\right)\)
2)
a) Nhớ ghi ĐK vào nhá, lười quá :V\(\dfrac{x^2-16}{4x-x^2}=-\dfrac{\left(x-4\right)\left(x+4\right)}{x^2-4x}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(x-4\right)}=\dfrac{x+4}{x}\)
b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)
\(=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)
c) \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+3\right)^3}{y\left(x+y\right)^2}\) ( câu này có gì đó sai sai )
d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)
\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)
e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)
\(=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)
a) \(\left(x+\dfrac{1}{2}\right)^2-2x^2\)
\(=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-2x^2\)
\(=x^2+x+\dfrac{1}{4}-2x^2\)
\(=-x^2+x+\dfrac{1}{4}\)
b) \(\left(x-2y\right)^2-4y^2\)
\(=x^2-2\cdot x\cdot2y+\left(2y\right)^2-4y^2\)
\(=x^2-4xy+4y^2-4y^2\)
\(=x^2-4xy\)
c) \(\left(x+\dfrac{1}{2}y\right)^3\)
\(=x^3+3\cdot x^2\cdot\dfrac{1}{2}y+3\cdot x+\left(\dfrac{1}{2}y\right)^2+\left(\dfrac{1}{2}y\right)^3\)
\(=x^3+\dfrac{3}{2}x^2y+\dfrac{3}{4}xy^2+\dfrac{1}{8}y^3\)
d) \(\left(2x^2-3y\right)^3\)
\(=\left(2x^2\right)^3-3\cdot\left(2x^2\right)^2\cdot3y+3\cdot2x^2\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^6-36x^4y+54x^2y^2-27y^3\)
e) \(\left(x^2+y\right)^2-\left(x+y\right)^2\)
\(=\left[\left(x^2\right)^2+2\cdot x^2\cdot y+y^2\right]-\left(x^2+2\cdot x\cdot y+y^2\right)\)
\(=\left(x^4+2x^2y+y^2\right)-\left(x^2+2xy+y^2\right)\)
\(=x^4+2x^2y+y^2-x^2-2xy-y^2\)
\(=x^4+2x^2y-x^2-2xy\)
a: \(=x^3+4x^2+16x+64\)
b: \(=8x^3-60x^2+150x-125\)
c: \(=\dfrac{1}{8}-\dfrac{3}{4}x^2+\dfrac{3}{2}x-x^3\)
d: \(=-\left(27x^3+54x^2y+36xy^2+8y^3\right)\)
f: \(=x^3+x^2y^2+\dfrac{1}{3}xy^2+\dfrac{1}{27}y^6\)
Câu 1:
\(\text{a) }\dfrac{x^2-xy}{3xy-3y^2}=\dfrac{x\left(x-y\right)}{3y\left(x-y\right)}=\dfrac{x}{3y}\)
\(\text{b) }\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\\ =\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\\ =\dfrac{2a\left(x-1\right)^2}{5b\left(1-x\right)\left(1+x\right)}\\ =-\dfrac{2a\left(x-1\right)^2}{5b\left(x-1\right)\left(1+x\right)}\\ =-\dfrac{2a\left(x-1\right)}{5b\left(x+1\right)}\\ =-\dfrac{2ax-2a}{5bx+5b}\)
\(\text{c) }\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)
\(\text{d) }\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)
\(\text{e) }\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\\ =\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\\ =\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x+y\right)^3}\\ =\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\\ =\dfrac{x^3+y^3}{x^4-xy^3}\)
Câu 3:
\(\text{ a) }\dfrac{\left(a+b\right)^2-c^2}{a+b+c}=\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{a+b+c}=a+b-c\)
\(\text{b) }\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\\ =\dfrac{\left(a^2+2ab+b^2\right)-c^2}{\left(a^2+2ac+c^2\right)-b^2}\\ =\dfrac{\left(a+b\right)^2-c^2}{\left(a+c\right)^2-b^2}\\ =\dfrac{\left(a+b+c\right)\left(a+b-c\right)}{\left(a+c+b\right)\left(a+c-b\right)}\\ =\dfrac{a+b-c}{a-b+c}\)
\(\text{c) }\dfrac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\\ =\dfrac{2x^3-x^2-6x^2+3x-15x+45}{3x^3-10x^2-9x^2+3x+30x-9}\\ =\dfrac{\left(2x^3-x^2-15x\right)-\left(6x^2-3x-45\right)}{\left(3x^3-10x^2+3x\right)-\left(9x^2-30x+9\right)}\\ =\dfrac{x\left(2x^2-x-15\right)-3\left(2x^2-x-15\right)}{x\left(3x^2-10x+3\right)-3\left(3x^2-10x+3\right)}\\ =\dfrac{\left(x-3\right)\left(2x^2-x-15\right)}{\left(x-3\right)\left(3x^2-10x+3\right)}\\ =\dfrac{\left(x-3\right)\left(2x^2-6x+5x-15\right)}{\left(x-3\right)\left(3x^2-9x-x+3\right)}\\ =\dfrac{\left(x-3\right)\left[\left(2x^2-6x\right)+\left(5x-15\right)\right]}{\left(x-3\right)\left[\left(3x^2-9x\right)-\left(x-3\right)\right]}\\ =\dfrac{\left(x-3\right)\left[x\left(x-3\right)+5\left(x-3\right)\right]}{\left(x-3\right)\left[3x\left(x-3\right)-\left(x-3\right)\right]}\\ =\dfrac{\left(x-3\right)\left(x-3\right)\left(x+5\right)}{\left(x-3\right)\left(x-3\right)\left(3x-1\right)}\\ =\dfrac{x+5}{3x-1}\)
Lời giải:
a) \(\frac{45x(3-x)}{15(x-3)^3}=\frac{-45x(x-3)}{15(x-3)^3}=\frac{-3x}{(x-3)^2}\)
b) \(\frac{36(x-2)^3}{32-16x}=\frac{36(x-2)^3}{-16(x-2)}=\frac{-9}{4}(x-2)^2\)
c) \(\frac{x^2-xy}{5y^2-5xy}=\frac{x(x-y)}{-5y(x-y)}=\frac{x}{-5y}\)
d) \(\frac{y^2-x^2}{x^3-3x^2y+3xy^2-y^3}=\frac{-(x^2-y^2)}{(x-y)^3}=\frac{-(x-y)(x+y)}{(x-y)^3}=\frac{-(x+y)}{(x-y)^2}\)
Bài 1 :
a, \(4\left(-3\text{x}\right)yx^5=-12x^6y\)
Hệ số : -12 , Biến : \(x^6y\)
b, \(7\text{x}y^5\left(-5\text{x}^3y^2\right)=-35\text{x}^4y^7\)
Hệ số : -35 , Biến : \(x^4y^7\)
c, \(-\left[-23\text{a}b\text{x}^3\left(-y\right)\right]=-23ab\text{x}^3y\)
Hệ số : -23 , Biến : \(ab\text{x}^3y\)
d, \(\left(-3\text{a}y^3\right)\left(-5b^2xy\right)=3\text{a}y^3\cdot5b^2xy=15\text{a}b^2xy^4\)
Hệ số : 15 , Biến : \(ab^2xy^4\)
Bài 2 :
a, \(x^4y^5z\)có Bậc là 10
b, \(-\left(-7\text{x}^7y\right)=7\text{x}^7y\)có bậc là 8
c,
b, \(-41\left(x^3y^2\right)^2=-41\text{x}^6y^4\)có bậc là 10
d, \(-2\frac{1}{3}x^3\left(xy^2\right)^3=-\frac{7}{3}x^3.x^3.y^6=-\frac{7}{3}x^6y^6\)có bậc là 12
a: \(\dfrac{5}{2x+6}=\dfrac{5\left(x-3\right)}{2\left(x+3\right)\left(x-3\right)}\)
3/x^2-9=6/2(x+3)(x-3)
b: \(\dfrac{2x}{x^2-8x+16}=\dfrac{2x}{\left(x-4\right)^2}=\dfrac{6x^2}{3x\left(x-4\right)^2}\)
\(\dfrac{x}{3x^2-12x}=\dfrac{x}{3x\left(x-4\right)}=\dfrac{x\left(x-4\right)}{3x\left(x-4\right)^2}\)
c: \(\dfrac{x+y}{x}=\dfrac{\left(x+y\right)\cdot\left(x-y\right)}{x\left(x-y\right)}\)
x/x-y=x^2/x(x-y)
e: \(\dfrac{1}{x+2}=\dfrac{2x-x^2}{x\left(x+2\right)\left(2-x\right)}\)
\(\dfrac{8}{2x-x^2}=\dfrac{8\left(x+2\right)}{x\left(2-x\right)\left(2+x\right)}\)
a: \(2xy^2\cdot\left(-\dfrac{5}{2}x^2y\right)=-5x^3y^3\)
Hệ số là -5
Phần biến là \(x^3;y^3\)
b: \(\dfrac{2}{3}ax^2y^3\cdot xy^3=\dfrac{2}{3}ax^3y^6\)
Hệ số là \(\dfrac{2}{3}a\)
Phần biến là \(x^3;y^6\)
bạn nào lm dc mik chk ban đấy 100 like