bieu thuc \(\frac{3+\frac{1}{x-1}}{2-\frac{x^2+1}{x^2-1}}\)bang phan thuc
Những câu hỏi liên quan
1) Cho bieu thuc A=\(3+\frac{2}{x-1}\). Tinh gia tri cua bieu thuc A khi |2x-3|=1
2) Rut gon bieu thuc B=\(\frac{x}{x-1}\)-\(\frac{x-5}{x+1}\)-\(\frac{3-x}{1-x^2}\)
3) Tim cac gia tri nguyen cua x de bieu thuc \(\frac{B}{A}\)co gia tri nguyen duong
Cho bieu thuc: \(p=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
a) Tim DKXD cua bieu thuc p
b) Rut gon bieu thuc p
1.cho bieu thuc A=\(\left(\frac{2}{x-2}+\frac{1}{x+2}\right):\frac{1}{x+2}\)
a.rút gọn bieu thuc A
b.tinh gia tri cua A tại x,biet x=1
2.tim x nguyen de gia tri cua bieu thuc A nguyen
a.\(A=\frac{3}{x+2}\)
b.\(A=\frac{x+3}{x-2}\)
Cho bieu thuc A = \(^{x2+4x+3}\)
a Tinh gia tri bieu thuc tai x= \(\frac{-1}{2}\)
b Tinh gia tri x de bieu thuc A bang 0
a. Tại x=\(\frac{-1}{2}\), ta có:
\(\left(\frac{-1}{2}\right)^2+4.\left(\frac{-1}{2}\right)+3=\frac{1}{4}+\left(-2\right)+3=\frac{5}{4}\)
b. Ta có:
\(x^2+4x+3=0\)
\(\Rightarrow x^2+x+3x+3=0\)
\(\Rightarrow\left(x^2+x\right)+\left(3x+3\right)=0\)
\(\Rightarrow x\left(x+1\right)+3\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x+3\right)=0\)
\(\Rightarrow\hept{\begin{cases}x+1=0\\x+3=0\end{cases}\Rightarrow\hept{\begin{cases}x=-1\\x=-3\end{cases}}}\)
Vậy \(x=-1;x=-3\)
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\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\)\(\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
Rut gon bieu thuc
tum x de bieu thuc = \(\frac{-1}{7}\)
\(đkxđ\Leftrightarrow\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)
\(A=\)\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}.\)
\(=\frac{15\sqrt{x}-11}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\)\(\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(=\frac{15\sqrt{x}-11-\left(3\sqrt{x}-2\right)\left(\sqrt{x}+3\right)-\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{15\sqrt{x}-11-3x-7\sqrt{x}+6-2x-\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{-5x+7\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)\(=\frac{-5x+5\sqrt{x}+2\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{-5\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)\(=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}\)
\(A=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}\)
\(\Rightarrow\frac{-5\sqrt{x}+2}{\sqrt{x}+3}=-\frac{1}{7}\Rightarrow-7\left(-5\sqrt{x}+2\right)=\sqrt{x}+3\)
\(\Rightarrow35\sqrt{x}-14=\sqrt{x}+3\)
\(\Rightarrow34\sqrt{x}=17\)
\(\Rightarrow\sqrt{x}=\frac{1}{2}\Rightarrow x=\frac{1}{4}\left(tm\right)\)
Vậy với \(x=\frac{1}{4}\)thì \(A=-\frac{1}{7}\)
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1.cho phan thuc P=\(\frac{5x-4y}{5x+4y}\)voi 25x2+16y2=50xy.khi do gia tri cua bieu thuc P=\(\frac{1+P^2}{1-P^2}\)la
2.gia tri lon nhat cua bieu thuc B=\(\frac{14}{\frac{x^2}{4}-3x+16}la\)
3.gia tri cua a de da thuc A=2x3+7x2+ax+3 chia het cho B=(x+1)2la a=?
\(25x^2+16y^2=50xy\)
\(\Leftrightarrow\) \(\left(5x+4y\right)^2-40xy=50xy\)
\(\Leftrightarrow\) \(\left(5x+4y\right)^2=90xy\)
Mặt khác, ta cũng có: \(25x^2+16y^2=50xy\)
\(\Leftrightarrow\) \(\left(5x-4y\right)^2=10xy\)
Do đó:
\(P^2=\frac{\left(5x-4y\right)^2}{\left(5x+4y\right)^2}=\frac{10xy}{90xy}=\frac{1}{9}\)
Vậy, \(P'=\frac{1+\frac{1}{9}}{1-\frac{1}{9}}=1\frac{1}{4}\)
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1)
\(25x^2-40xy+16y^2=10xy\Leftrightarrow\left(5x-4y\right)^2=10xy\)
\(25x^2+40xy+16y^2=10xy\Leftrightarrow\left(5x+4y\right)^2=90xy\)
\(P^2=\frac{1}{9}\Leftrightarrow Q=\frac{1+P^2}{1-P^2}=\frac{1+\frac{1}{81}}{1-\frac{1}{81}}=\frac{82}{80}=\frac{41}{40}\)
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I Cho bieu thucA ( frac{2x+1}{2x-1}- frac{2x-1}{2x+1}) : frac{8x}{3-6x}( voi x khac + - frac{1}{2}x khax 0 )a . Rut gon bieu thuc Ab . Tim x de A frac{3}{-4031}II Cho bieu thuc B ( frac{1}{1-x}+frac{2}{x+1}-frac{5-x}{1-x^2}) : frac{1-2x}{x^2-4}a . Rut gon bieu thuc Bb . Tìm giá trị nguyên của x để giá trị của biểu thức B là số nguyên
Đọc tiếp
I> Cho bieu thuc
A = ( \(\frac{2x+1}{2x-1}\)- \(\frac{2x-1}{2x+1}\)) : \(\frac{8x}{3-6x}\)( voi x khac + - \(\frac{1}{2}\)x khax 0 )
a . Rut gon bieu thuc A
b . Tim x de A = \(\frac{3}{-4031}\)
II> Cho bieu thuc
B = ( \(\frac{1}{1-x}\)+\(\frac{2}{x+1}\)-\(\frac{5-x}{1-x^2}\)) : \(\frac{1-2x}{x^2-4}\)
a . Rut gon bieu thuc B
b . Tìm giá trị nguyên của x để giá trị của biểu thức B là số nguyên
1) Cho bieu thuc: \(B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\left(x\ge0,x\ne16\right)\)
a) Cho bieu thuc A= \(\frac{\sqrt{x}+4}{\sqrt{x}+2}\) ; voi cac cua bieu thuc A va B da cho, hay tim cac gia tri cua x nguyen de gia tri cua bieu thuc B(A;-1) la so nguyen
dung dinh nghia 2 phan thuc bang nhau chung minh cac phan thuc sau bang nhau
\(\frac{2-x}{2+x}=\frac{x^2-4x+4}{4-x^2}\)
\(\frac{x^3-9x}{15-5x}=\frac{-x^2-3x}{5}\)
https://i.imgur.com/cZP2lBs.jpg
Lời giải:
\(\frac{x^2-4x+4}{4-x^2}=\frac{x^2-2.2.x+2^2}{2^2-x^2}=\frac{(x-2)^2}{(2-x)(2+x)}=\frac{(2-x)^2}{(2-x)(2+x)}=\frac{2-x}{2+x}\) (đpcm)
\(\frac{x^3-9x}{15-5x}=\frac{x(x^2-9)}{5(3-x)}=\frac{x(x-3)(x+3)}{5(3-x)}=\frac{-x(3-x)(x+3)}{5(3-x)}=\frac{-x(x+3)}{5}=\frac{-x^2-3x}{5}\) (đpcm)