Bài 1: \(\dfrac{x}{3}=\dfrac{y}{5}\) Tính C= \(\dfrac{5x^2+3y^2}{10x^2-3y^2}\)
Bài 2: Tìm số nguyên x, y biết : \(x-2xy+y-3=0\)
Bài 3: x+y=2
Tính P= \(x^2+xy^2-2x^2-xy-y^2+3y+x+2017\\ \)
Bài 1 : Tính giá trị biểu thức sau , biết x+y-2=0
a ) M = x^3+x^2y+2x^2-xy-y^2+3y+x-1
b ) N= x^3-2x^2-xy^2+2xy+2y+2x-2
c ) P = x^4+2x^3y-2x^3+x^2y^2-2x^2y-x*(x+y )+2x+3
Biến đổi mỗi đa thức theo hướng làm xuất hiện thừa số x+y-2 \(M=x^3+x^2y-2x^2-xy-y^2+3y+x-1\)
\(M=x^3+x^2y-2x^2-xy-y^2+\left(2y+y\right)+x-\left(-2+1\right)\)
\(M=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-2\right)+1\)
\(M=\left(x^2.x+x^2.y-2x^2\right)-\left(x.y+y.y-2y\right)+\left(x+y-2\right)+1\)
\(M=x^2.\left(x+y-2\right)-y.\left(x+y-2\right)+\left(x+y-2\right)+1\)
\(M=x^2.0+y.0+0+1\)
\(M=1\)
\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-2\)
\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-\left(-4+2\right)\)
\(N=\left(x^3+x^2y-2x^2\right)-\left(x^2y+xy^2-2xy\right)+\left(2x+2y-4\right)+2\)
\(N=\left(x^2x+x^2y-2x^2\right)-\left(xyx+xyy-2xy\right)+\left(2x+2y-4\right)+2\)
\(N=x^2\left(x+y-2\right)-xy\left(x+y-2\right)+2\left(x+y-2\right)+2\)
\(N=x^2.0-xy.0+2.0+2\)
\(N=2\)
\(P=x^4+2x^3y-2x^3+x^2y^2-2x^2y-x\left(x+y\right)+2x+3\)
\(P=\left(x^4+x^3y-2x^3\right)+\left(x^3y+x^2y^2-2x^2y\right)-\left(x^2+xy-2x\right)+3\)\(P=\left(x^3x+x^3y-2x^3\right)+\left(x^2y.x+x^2yy-2x^2y\right)-\left(xx+xy-2x\right)+3\)
\(P=x^3\left(x+y-2\right)+x^2y\left(x+y-2\right)-x\left(x+y-2\right)+3\)
\(P=x^3.0+x^2y.0-x.0+3\)
\(P=3\)
Tích mình nha!
Làm tính trừ phân thức :
a) \(\dfrac{3x-2}{2xy}-\dfrac{7x-4}{2xy}\)
b) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)
c) \(\dfrac{4x+7}{2x+2}-\dfrac{3x+6}{2x+2}\)
d) \(\dfrac{9x+5}{2\left(x-1\right)\left(x+3\right)^2}-\dfrac{5x-7}{2\left(x-1\right)\left(x+3\right)^2}\)
e) \(\dfrac{xy}{x^2-y^2}-\dfrac{x^2}{y^2-x^2}\)
f) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\)
g)\(\dfrac{x}{5x+5}-\dfrac{x}{10x-10}\)
h) \(\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\)
\(\dfrac{1}{3x-3y};\dfrac{1}{x^2-2xy+y^{ }2}\)
\(\dfrac{3}{x^2-3x};\dfrac{5}{2x-6}\)
\(\dfrac{x}{x+3};\dfrac{1}{3-x};\dfrac{1}{x^2-9}\)
\(\dfrac{1}{x^2+xy};\dfrac{1}{xy-ỳ^2};\dfrac{2}{y^2-x^2}\)
giúp với ạ :((
\(a,\dfrac{1}{3x-3y}=\dfrac{x-y}{3\left(x-y\right)^2};\dfrac{1}{x^2-2xy+y^2}=\dfrac{3}{3\left(x-y\right)^2}\\ b,\dfrac{3}{x^2-3x}=\dfrac{6}{2x\left(x-3\right)};\dfrac{5}{2x-6}=\dfrac{5x}{2x\left(x-3\right)}\\ c,\dfrac{x}{x+3}=\dfrac{x^2-3x}{\left(x-3\right)\left(x+3\right)};\dfrac{1}{3-x}=\dfrac{-x-3}{\left(x-3\right)\left(x+3\right)};\dfrac{1}{x^2-9}=\dfrac{1}{\left(x-3\right)\left(x+3\right)}\)
\(d,\dfrac{1}{x^2+xy}=\dfrac{xy-y^2}{xy\left(x+y\right)\left(x-y\right)};\dfrac{1}{xy-y^2}=\dfrac{x^2+xy}{xy\left(x-y\right)\left(x+y\right)};\dfrac{2}{y^2-x^2}=\dfrac{-2xy}{xy\left(x-y\right)\left(x+y\right)}\)
Cho tỉ lệ thức \(\dfrac{x}{y}=\dfrac{2}{3}\). Tính giá trị của các biểu thức sau:
\(A=\dfrac{x+5y}{3x-2y}-\dfrac{2x-3y}{4x+5y}\)
\(B=\dfrac{2x^2-xy+3y^2}{3x^2+2xy+y^2}\)
Lời giải:
$\frac{x}{y}=\frac{2}{3}\Rightarrow \frac{x}{2}=\frac{y}{3}$. Đặt $\frac{x}{2}=\frac{y}{3}=k$ thì:
$x=2k; y=3k$
Khi đó: $3x-2y=3.2k-3.2k=0$. Mẫu số không thể bằng $0$ nên $A$ không xác định. Bạn xem lại.
$B=\frac{2(2k)^2-2k.3k+3(3k)^2}{3(2k)^2+2.2k.3k+(3k)^2}=\frac{29k^2}{33k^2}=\frac{29}{33}$
Bài 2 :
a) Tìm các số nguyên x,y biết rằng \(\dfrac{x}{7}-\dfrac{1}{2}=\dfrac{y}{y+1}\)
b) Cho \(\dfrac{x}{3}=\dfrac{y}{4}\) và \(\dfrac{y}{5}=\dfrac{z}{6}\). Tính A = \(\dfrac{2x+3y+4z}{3x+4y+5z}\)
c) Tìm giá trị nhỏ nhất của biểu thức B, biết rằng
\(B=\left|7x-5y\right|+\left|2z-3x\right|+\left|xy+yz+zx-2000\right|\)
b, Ta có : \(\dfrac{x}{3}=\dfrac{y}{4};\dfrac{y}{5}=\dfrac{z}{6}\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{24}\)
Đặt \(x=15k;y=20k;z=24k\)
Thay vào A ta được : \(A=\dfrac{30k+60k+96k}{45k+80k+120k}=\dfrac{186k}{245k}=\dfrac{186}{245}\)
a, \(\dfrac{x}{7}-\dfrac{1}{2}=\dfrac{y}{y+1}\Leftrightarrow\dfrac{2x-7}{14}=\dfrac{y}{y+1}\Rightarrow\left(2x-7\right)\left(y+1\right)=14y\)
\(\Leftrightarrow2xy+2x-7y-7=14y\Leftrightarrow2xy+2x-21y-7=0\)
\(\Leftrightarrow2x\left(y+1\right)-21\left(y+1\right)+14=0\Leftrightarrow\left(2x-21\right)\left(y+1\right)=-14\)
\(\Rightarrow2x-21;y+1\inƯ\left(-14\right)=\left\{\pm1;\pm2;\pm7;\pm14\right\}\)
2x - 21 | 1 | -1 | 2 | -2 | 7 | -7 | 14 | -14 |
y + 1 | -14 | 14 | -7 | 7 | -2 | 2 | -1 | 1 |
x | 11 | 10 | loại | loại | 14 | 7 | loại | loại |
y | -15 | 13 | loại | loại | -3 | 1 | loại | loại |
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
Tìm GTNN:
A=\(\sqrt{25-10x+x^2}-\sqrt{x^2-6x+9}\)
B:\(\dfrac{1}{2x^2-x+3}\)
C: x2 - 2xy + 3y2 - 2x + 2017
D: x-\(\sqrt{x-2015}\)
E:\(\dfrac{2x+1}{x^2}\)
F: \(\dfrac{5x^2-4x+4}{x^2}\)
G=(x+1)(x+2)2(x+3)
H= X2-5x+y2+xy-4y+2014
I= x2 +xy +y2-3x-3y +2002
K=\(\sqrt{x^2-6x+2y^2+4y+11}+\sqrt{x^2+2x+3y^2+6y+4}\)
2/ Thực hiện phép tính
a/ (x-y)(x2+xy+y2)
b/(x2-2xy+y2)(x-y)
c/ (x2y2-\(\dfrac{1}{3}\) xy+3y)(x-3y)
d/(\(\dfrac{1}{5}\)x-1)(x2 -5x+2)
a ) \(\left(x-y\right)\left(x^2+xy+y^2\right)=x^3-y^3\)
b ) \(\left(x^2-2xy+y^2\right)\left(x-y\right)=\left(x-y\right)^2\left(x-y\right)=\left(x-y\right)^3\)
c ) \(\left(x^2y^2-\dfrac{1}{3}xy+3y\right)\left(x-3y\right)\)
\(=\left(x^2y^2-\dfrac{1}{3}xy+3y\right)x-3y\left(x^2y^2-\dfrac{1}{3}xy+3y\right)\)
\(=x^3y^2-\dfrac{1}{3}x^2y+3xy-3x^2y^3+xy^2-9y^2\)
d ) \(\left(\dfrac{1}{5}x-1\right)\left(x^2-5x+2\right)\)
\(=\dfrac{1}{5}x\left(x^2-5x+2\right)-x^2+5x-2\)
\(=\dfrac{1}{5}x^3-x^2+\dfrac{2}{5}x-x^2+5x-2\)
\(=\dfrac{1}{5}x^3-2x^2+\dfrac{27}{5}x-2\)
\(a,\left(x-y\right)\left(x^2+xy+y^2\right)=x^3-y^3\)
1.Tính \(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)
2.Phân tích đa thức thành nhân tử
1)\(\left(x^2y^2-8\right)-1\)
2)\(x^3y-2x^2y+xy-xy^3\)
3)\(x^3-2x^2y+xy^2\)
4)\(x^2+2x-y^2+1\)
5)\(x^2+2x-4y^2+1\)
6)\(x^2-6x-y^2+9\)
bài 1: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)
\(=\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x-x^2-2x}{\left(x-2\right)\left(x+2\right)}=-\dfrac{4x}{x^2-4}\)
Bài 2:
1: \(x^2y^2-8-1\)
\(=x^2y^2-9\)
\(=\left(xy-3\right)\left(xy+3\right)\)
2: \(x^3y-2x^2y+xy-xy^3\)
\(=xy\cdot x^2-xy\cdot2x+xy\cdot1-xy\cdot y^2\)
\(=xy\left(x^2-2x+1-y^2\right)\)
\(=xy\left[\left(x-1\right)^2-y^2\right]\)
\(=xy\left(x-1-y\right)\left(x-1+y\right)\)
3: \(x^3-2x^2y+xy^2\)
\(=x\cdot x^2-x\cdot2xy+x\cdot y^2\)
\(=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\)
4: \(x^2+2x-y^2+1\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
5: \(x^2+2x-4y^2+1\)
\(=\left(x^2+2x+1\right)-4y^2\)
\(=\left(x+1\right)^2-4y^2\)
\(=\left(x+1-2y\right)\left(x+1+2y\right)\)
6: \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)