Thực hiện phép tính
\(\frac{4-x^2}{x-3}\)\(+\)\(\frac{2x-2x^2}{3-x}\)\(+\)\(\frac{5-4x}{x-3}\)
5,Thực hiện phép tính
1,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
2,\(\frac{1}{1-x}+\frac{2x}{x^2-1}\)
3,\(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
4,\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}\)
5,\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
1,\(\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x}{x\left(2x+6\right)}+\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x+x-6}{x\left(2x+6\right)}\)=\(\frac{4x-6}{x\left(2x+6\right)}=\frac{2\left(2x-3\right)}{x\left(2x+6\right)}\)
2, \(\frac{1}{1-x}-\frac{2x}{1-x^2}\)=\(\frac{1+x}{\left(1-x\right)\left(1+x\right)}+\frac{2x}{\left(1-x\right)\left(1+x\right)}\)=\(\frac{1+x+2x}{\left(1-x\right)\left(1+x\right)}=\frac{3x+1}{\left(1-x\right)\left(1+x\right)}\)
3,1/x(y-x)-1/y(y-x)=y/xy(y-x)-x/xy(y-x)=(y-x)/xy(x-y)=1/xy
Bài 1 : thực hiện phép tính
a) \(\frac{3x+5}{2.\left(x-1\right)}+\frac{4}{x-2}\)
b) \(\frac{2x^2+1}{4x^2-2x}+\frac{3-3x}{1-2x}+\frac{3}{2x}\)
a) \(\frac{3x+5}{2\left(x-1\right)}+\frac{4}{x-2}=\frac{\left(3x+5\right)\left(x-2\right)+4\cdot2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)}=\frac{3x^2-6x+5x-10+8x-8}{2\left(x-1\right)\left(x-2\right)}\)
\(=\frac{3x^2+7x-18}{2\left(x-1\right)\left(x-2\right)}\)
b) \(\frac{2x^2+1}{4x^2-2x}+\frac{3-3x}{1-2x}+\frac{3}{2x}=\frac{2x^2+1+4x\left(3-3x\right)+2\cdot3\left(1-2x\right)}{4x\left(1-2x\right)}=\frac{2x^2+1+12-12x+6-12x}{4x\left(1-2x\right)}\)\(=\frac{2x^2-24x+19}{4x\left(1-2x\right)}\)
Đề này... bạn xem lại đi. Chứ thế này thì dùng máy tính cũng không làm nổi T-T
Thực hiện phép tính
a)) \(\frac{3}{2x}+\frac{3x+3}{2x-1}+\frac{2x^2+1}{4x^2-2x}\)
b)) \(\frac{x^3+2x}{x^3+1}+\frac{2x}{x^2-x+1}+\frac{1}{x+1}\)
c)) \(\frac{4}{x+2}+\frac{2}{x-2}+\frac{5x-6}{4-x^2}\)
Bạn nào biết làm thì giúp mình nhé. Mình tick cho nè. Thanks
mk ko biết làm
xin lỗi bn nhae
xin lỗi vì đã ko giúp được bn
chcus bn học gioi!
nhae@@@
mình không biết làm
tk nhé@@@@@@@@@@@@@@@@@@@@
LOL
hihi
a) ... \(=\frac{3\left(2x-1\right)+2x\left(3x+3\right)+2x^2+1}{2x\left(2x-1\right)}=\frac{6x-3+6x^2+6x+2x^2+1}{2x\left(2x-1\right)}\)
\(=\frac{8x^2+12x-2}{2x\left(2x-1\right)}=\frac{4x^2+6x-1}{x\left(2x-1\right)}\)(hình như hết đơn giản được rồi, kết quả tạm vậy bạn nhé!)
b) ... \(=\frac{x^3+2x+2x\left(x+1\right)+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\frac{x^3+2x+2x^2+2x+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\frac{x^3+3x^2+3x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\frac{\left(x+1\right)^3}{\left(x+1\right)\left(x^2-x+1\right)}=\frac{x^2+2x+1}{x^2-x+1}\)
c) ... \(=\frac{4\left(x-2\right)+2\left(x+2\right)-5x+6}{\left(x-2\right)\left(x+2\right)}=\frac{4x-8+2x+4-5x+6}{\left(x-2\right)\left(x+2\right)}=\frac{x+2}{\left(x-2\right)\left(x+2\right)}=\frac{1}{x-2}\)
Áp dụng quy tắc đổi dấu để các phân thức có cùng mẫu thức rồi thực hiện phép cộng phân thức:
a) \(\frac{16+x}{x^2-2x}+\frac{18}{2x-x^2}\)
b)\(\frac{2y}{2x^2-xy}+\frac{4x}{xy-2x^2}\)
c)\(\frac{4-x^2}{x-3}+\frac{2x-2x^2}{3-x}+\frac{5-4x}{x-3}\)
Mong 500 ae giúp ạ ^^
\(=\frac{16+x}{x^2-2x}-\frac{18}{x^2-2x}\)
\(=\frac{16+x-18}{x\left(x-2\right)}\)
\(=\frac{-2+x}{x\left(x-2\right)}\)
a) \(\frac{16+x}{x^2-2x}+\frac{18}{2x-x^2}=\frac{16+x-18}{x^2-2x}=\frac{x-2}{x\left(x-2\right)}=\frac{1}{x}\)
b) \(\frac{2y}{2x^2-xy}+\frac{4x}{xy-2x^2}=\frac{2y-4x}{2x^2-xy}=\frac{-2\left(2x-y\right)}{x\left(2x-y\right)}=\frac{-2}{x}\)
c) \(\frac{4-x^2}{x-3}+\frac{2x-2x^2}{3-x}+\frac{5-4x}{x-3}=\frac{4-x^2+2x^2-2x+5-4x}{x-3}=\frac{x^2-6x+9}{x-3}=\frac{\left(x-3\right)^2}{x-3}=x-3\)
a)
\(\frac{16+x}{x^2-2x}+\frac{18}{2x-x^2}=\frac{16+x}{x^2-2x}-\frac{18}{x^2-2x}\)
\(=\frac{16+x-18}{x\left(x-2\right)}=\frac{x-2}{x\left(x-2\right)}=\frac{1}{x}\)
b) \(\frac{2y}{2x^2-xy}+\frac{4x}{xy-2x^2}=\frac{2y}{2x^2-xy}-\frac{4x}{2x^2-xy}\)
\(=\frac{2y-4x}{x\left(2x-y\right)}=\frac{2\left(y-2x\right)}{x\left(2x-y\right)}=-\frac{2}{x}\)
c) \(\frac{4-x^2}{x-3}+\frac{2x-2x^2}{3-x}+\frac{5-4x}{x-3}\)\(=\frac{4-x^2}{x-3}-\frac{2x-2x^2}{x-3}+\frac{5-4x}{x-3}\)
\(=\frac{4-x^2-2x+2x^2+5-4x}{x-3}\)\(=\frac{x^2-6x+9}{x-3}=\frac{\left(x-3\right)^2}{x-3}=x-3\)
Thực hiện phép tính
a) \(\left(\frac{2x+1}{2x-2}+\frac{3}{x^2-1}-\frac{x+3}{2x+2}\right).\frac{4x^2-4}{3}\)
b) \(\left(\frac{5x+2}{x^2-10x}+\frac{5x-2}{x^2+10x}\right).\frac{x^2-100}{x^2+4}\)
c) \(\frac{1}{x-1}-\frac{x^3-x}{x^2+1}.\left(\frac{1}{x^2-2x+1}+\frac{1}{1-x^2}\right)\)
Thực hiện phép tính:
a) \(\frac{1}{x}-\frac{1}{x+1}\)
b)\(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}\)
d) \(\frac{2x-1}{x}-\frac{2x+5}{3x-4x^2}+\frac{2x^2+x+3}{3x-4x^2}\)
e) \(\frac{x}{2x+1}+\frac{1}{4x^2-1}-\frac{x-2}{2x-1}\)
giúp mình với mình cần gấp ! Help me ===)
\(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x^2+x}\)
b, \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{y^2-xy-xy+x^2}{\left(xy-x^2\right)\left(y^2-xy\right)}=\frac{x^2+y^2}{xy^3-xyxy-xyxy+x^3y}\)Tu rut gon tiep
c, tt
d, cx r
a) \(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}\)
\(=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x\left(x+1\right)}\)
b) \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)
\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)
c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}=\frac{9x-3}{4x-1}+\frac{3x}{4x-1}\)
\(=\frac{9x-3+3x}{4x-1}=\frac{6x-3}{4x-1}\)
\(a,\frac{1}{x}-\frac{1}{x+1}\)
\(=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}=\frac{x+1-x}{x\left(x+1\right)}\)
\(=\frac{1}{x\left(x+1\right)}\)
\(b,\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
\(=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)
\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{x-y}{xy\left(x-y\right)}=\frac{1}{xy}\)
Thực hiện phép tính
\(\frac{4-x}{x^3+2x}\)\(-\)\(\frac{x+5}{x^3-x^2+2x-2}\)
\(\frac{4-x}{x^3+2x}-\frac{x+5}{x^3-x^2+2x-2}\)( ĐKXĐ : \(x\ne1\))
\(=\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{x^2\left(x-1\right)+2\left(x-1\right)}\)
\(=\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{\left(4-x\right)\left(x-1\right)}{x\left(x-1\right)\left(x^2+2\right)}-\frac{x\left(x+5\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4}{x\left(x-1\right)\left(x^2+2\right)}-\frac{x^2+5x}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4-\left(x^2+5x\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4-x^2-5x}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2x^2-4}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2\left(x^2+2\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2}{x\left(x-1\right)}=\frac{-2}{x\left(x-1\right)}\)
Đang đánh máy thì bấm gửi -..-
\(\frac{4-x}{x^3+2x}-\frac{x+5}{x^3-x^2+2x-2}=\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{\left(4-x\right)\left(x-1\right)}{x\left(x+1\right)\left(x^2+2\right)}-\frac{x\left(x+5\right)}{x\left(x+1\right)\left(x^2+2\right)}=\frac{\left(4-x\right)\left(x-1\right)-x\left(x+5\right)}{x\left(x+1\right)\left(x^2+2\right)}\)
\(=\frac{-2x^2-4}{x\left(x-1\right)\left(x^2+2\right)}=\frac{-2}{x\left(x-1\right)}\)
thực hiện phép tính sau:
a)\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
b)\(5+\frac{96}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
\(a,\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
\(\frac{x\left(x+1\right)}{2\left(x-3\right)\left(x+1\right)}+\frac{x\left(x-3\right)}{2\left(x+1\right)\left(x-3\right)}=\frac{4x}{2\left(x+1\right)\left(x-3\right)}\)
\(x\left(x+1\right)+x\left(x-3\right)=4x\)
\(x^2+x+x^2-3x=4x\)
\(2x^2-2x=4x\)
\(2x^2-2x-4x=0\)
\(2x\left(x-3\right)=0\)
\(2x=0\Leftrightarrow x=0\)
hoặc
\(x-3=0\Leftrightarrow x=3\)
b) \(ĐKXĐ:x\ne\pm4\)
\(5+\frac{96}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
\(\Leftrightarrow5+\frac{96}{x^2-16}=\frac{2x-1}{x+4}+\frac{3x-1}{x-4}\)
\(\Leftrightarrow\frac{5\left(x^2-16\right)}{x^2-16}+\frac{96}{x^2-16}=\frac{\left(2x-1\right)\left(x-4\right)}{x^2-16}+\frac{\left(3x-1\right)\left(x+4\right)}{x^2-16}\)
\(\Rightarrow5\left(x^2-16\right)+96=\left(2x-1\right)\left(x-4\right)+\left(3x-1\right)\left(x+4\right)\)
\(\Leftrightarrow5x^2-80+96=2x^2-9x+4+3x^2+11x-4\)
\(\Leftrightarrow5x^2-2x^2-3x^2+9x-11x=4-4+80-96\)
\(\Leftrightarrow-2x=-16\)\(\Leftrightarrow x=8\)( thoả mãn ĐKXĐ )
Vậy tập nghiệm của phương trình là: \(S=\left\{8\right\}\)
Bài 1: Thực hiện phép tính:
a) \(\frac{4x-4}{x^2-4x-4}:\frac{x^2-1}{\left(2-x\right)^2}\)
b) \(\frac{2x+1}{2x^2-x}+\frac{32x^2}{1-4x^2}+\frac{1-2x}{2x^2+x}\)
c) \(\left(\frac{1}{x+1}+\frac{1}{x-1}-\frac{2x}{1-x^2}\right).\frac{x-1}{4x}\)
Bài 2:
1. Tìm n để đa thức x4 - x3 + 6x2 - x + n chia hết cho đa thức x2 - x + 5
2. Tìm n để đa thức 3x3 + 10x2 - 5 + n chia hết cho đa thức 3x + 1
Bài 3:
Cho biểu thức: N = ( 4x + 3 )2 - 2x ( x + 6 ) - 5 ( x - 2 ) ( x + 2 )
Chứng minh biểu thức n luôn dương.
Bài 1.
a)\(\frac{4x-4}{x^2-4x+4}\div\frac{x^2-1}{\left(2-x\right)^2}=\frac{4\left(x-1\right)}{\left(x-2\right)^2}\div\frac{\left(x-1\right)\left(x+1\right)}{\left(x-2\right)^2}=\frac{4\left(x-1\right)}{\left(x-2\right)^2}\times\frac{\left(x-2\right)^2}{\left(x-1\right)\left(x+1\right)}=\frac{4}{x+1}\)
b) \(\frac{2x+1}{2x^2-x}+\frac{32x^2}{1-4x^2}+\frac{1-2x}{2x^2+x}=\frac{2x+1}{x\left(2x-1\right)}+\frac{-32x^2}{4x^2-1}+\frac{1-2x}{x\left(2x+1\right)}\)
\(=\frac{\left(2x+1\right)\left(2x+1\right)}{x\left(2x-1\right)\left(2x+1\right)}+\frac{-32x^3}{x\left(2x-1\right)\left(2x+1\right)}+\frac{\left(1-2x\right)\left(2x-1\right)}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\frac{4x^2+4x+1}{x\left(2x-1\right)\left(2x+1\right)}+\frac{-32x^3}{x\left(2x-1\right)\left(2x+1\right)}+\frac{-4x^2+4x-1}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\frac{4x^2+4x+1-32x^3-4x^2+4x-1}{x\left(2x-1\right)\left(2x+1\right)}=\frac{-32x^3+8x}{x\left(2x-1\right)\left(2x+1\right)}\)
\(=\frac{-8x\left(4x^2-1\right)}{x\left(2x-1\right)\left(2x+1\right)}=\frac{-8x\left(2x-1\right)\left(2x+1\right)}{x\left(2x-1\right)\left(2x+1\right)}=-8\)
c) \(\left(\frac{1}{x+1}+\frac{1}{x-1}-\frac{2x}{1-x^2}\right)\times\frac{x-1}{4x}\)
\(=\left(\frac{1}{x+1}+\frac{1}{x-1}+\frac{2x}{x^2-1}\right)\times\frac{x-1}{4x}\)
\(=\left(\frac{x-1}{\left(x-1\right)\left(x+1\right)}+\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2x}{\left(x-1\right)\left(x+1\right)}\right)\times\frac{x-1}{4x}\)
\(=\left(\frac{x-1+x+1+2x}{\left(x-1\right)\left(x+1\right)}\right)\times\frac{x-1}{4x}\)
\(=\frac{4x}{\left(x-1\right)\left(x+1\right)}\times\frac{x-1}{4x}=\frac{1}{x+1}\)
Bài 3.
N = ( 4x + 3 )2 - 2x( x + 6 ) - 5( x - 2 )( x + 2 )
= 16x2 + 24x + 9 - 2x2 - 12x - 5( x2 - 4 )
= 14x2 + 12x + 9 - 5x2 + 20
= 9x2 + 12x + 29
= 9( x2 + 4/3x + 4/9 ) + 25
= 9( x + 2/3 )2 + 25 ≥ 25 > 0 ∀ x
=> đpcm