Rút gọn Q=(cănx/1-cănx + cănx/1+cănx) + 3-cănx/x-1
Bài 4 : Cho biểu thức Q=(x1−x+x1+x)+3−xx−1Q=\left(\frac{\sqrt{x}}{1-\sqrt{x}}+\frac{\sqrt{x}}{1+\sqrt{x}}\right)+\frac{3-\sqrt{x}}{x-1}Q=(1−xx+1+xx)+x−13−x ( với x≥0x\ge0x≥0 và xe1xe1xe1 )
a ) Rút gọn Q
b ) Tìm x để Q=−1Q=-1Q=−1
a) Q=(x1−x+x1+x)+3−xx−1(x≥0;xe1)Q=\left(\frac{\sqrt{x}}{1-\sqrt{x}}+\frac{\sqrt{x}}{1+\sqrt{x}}\right)+\frac{3-\sqrt{x}}{x-1}\left(x\ge0;xe1\right)Q=(1−xx+1+xx)+x−13−x(x≥0;xe1)
=−xx−1+xx+1+3−x(x−1)(x+1)=-\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{3-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=−x−1x+x+1x+(x−1)(x+1)3−x
=−x(x+1)+x(x−1)+3−x(x−1)(x+1)=\frac{-\sqrt{x}\left(\sqrt{x}+1\right)+\sqrt{x}\left(\sqrt{x}-1\right)+3-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=(x−1)(x+1)−x(x+1)+x(x−1)+3−x
=−x−x+x−x+3−x(x−1)(x+1)=\frac{-x-\sqrt{x}+x-\sqrt{x}+3-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=(x−1)(x+1)−x−x+x−x+3−x
=−3x+3(x−1)(x+1)=−3(x−1)(x−1)(x+1)=−3x+1=\frac{-3\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{-3\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=-\frac{3}{\sqrt{x}+1}=(x−1)(x+1)−3x+3=(x−1)(x+1)−3(x−1)=−x+13
b) Để Q=−1Q=-1Q=−1
⇔−3x+1=−1\Leftrightarrow-\frac{3}{\sqrt{x}+1}=-1⇔−x+13=−1
⇔x+1=3\Leftrightarrow\sqrt{x}+1=3⇔x+1=3
⇔x=2⇔x=4(tm)\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\left(tm\right)⇔x=2⇔x=4(tm)
Rút gọn biểu thức căn(15+2 căn5-căn(21-4 căn5))
rut gon bieu thuc a) 15+25−21−45\sqrt{15+2\sqrt{5}-\sqrt[]{21-4\sqrt{5}}}15+25−21−45
b)5−3−29−125\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}5−3−29−125
Rút gọn B= căn(căn5-căn3-căn29-12 căn5)
Rut gon :
B= 5−3−29−125\sqrt{\sqrt{5}-\sqrt{3}-\sqrt{29}-12\sqrt{5}}5−3−29−125
Rút gọn B=căn(x-2-2 căn(x-3))/căn(x-3)-1
bai 1 B=x−2−2x−3x−3−1B=\dfrac{\sqrt{x-2-2\sqrt{x-3}}}{\sqrt{x-3}-1}B=x−3−1x−2−2x−3
rut gon
Rút gọn căn5 - 2 căn3/ căn5 +căn3 - 2 căn5 +căn3/căn5-căn3
5−235+3−25+35−3\frac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\frac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}5+35−23−5−325+3Rút gọn
Rút gọn A=(1/cănx -2 -1/cănx):(cănx -1/cănx -2 - cănx +2/cănx +1)
A=(1x−2−1x):(x−1x−2−x+2x+1)A=\left(\frac{1}{\sqrt{x}-2}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}+1}\right)A=(x−21−x1):(x−2x−1−x+1x+2)
Rut gon A
Help me
Rút gọn P=(x cănx -1/x-1 - 3 cănx/cănx +1): x-cănx/4 cănx + 4
P= (xx−1x−1\frac{x\sqrt{x}-1}{x-1}x−1xx−1-3xx+1\frac{3\sqrt{x}}{\sqrt{x}+1}x+13x):x−x4x+4\frac{x-\sqrt{x}}{4\sqrt{x}+4}4x+4x−x
a, tìm x để P có nghĩa
b.rút gọn P
c,tìm x thuộc Z để P thuộc Z
Rút gọn căn(2 căn(5-5))^2+căn(24-8 căn5)
Tính ( rút gọn)
a.(25−5)2+24−85a.\sqrt{\left(2\sqrt{5-5}\right)^2}+\sqrt{24-8\sqrt{5}}a.(25−5)2+24−85
Rút gọn D=1/x- cănx - 2 cănx/ x -1 + 1/x+cănx
Rút gọn D
Với x> 0 và x khác 1
D = 1x−x−2xx−1+1x+x\frac{1}{x-\sqrt{x}}-\frac{2\sqrt{x}}{x-1}+\frac{1}{x+\sqrt{x}}x−x1−x−12x+x+x1
Rút gọn A=(2x+1/cănx^3 -1 - cănx/x-cănx +1).(3 cănx +cănx^3/x-3x - cănx)
rút gọn :
A = (2x+1x3−1−xx−x+1).(3x+x3x−3x−x)\left(\frac{2x+1}{\sqrt{x}^3-1}-\frac{\sqrt{x}}{x-\sqrt{x}+1}\right).\left(\frac{3\sqrt{x}+\sqrt{x}^3}{x-3x}-\sqrt{x}\right)(x3−12x+1−x−x+1x).(x−3x3x+x3−x)mk cần gấp ai giải nhanh hộ vs thanks
Rút gọn A=(1/a-căn a +1/căn a -1):căn(a+1)/a-2 căn a +1
Cho biểu thức A=(1a−a+1a−1):a+1a−2a+1A=\left(\frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1}\right):\frac{\sqrt{a+1}}{a-2\sqrt{a}+1}A=(a−a1+a−11):a−2a+1a+1 ( với a>0a>0a>0 và ae1ae1ae1 ).
a ) Rút gọn biểu thức A
b ) Tìm a để A=12A=\frac{1}{2}A=21