CHO BIỂU THỨC P=\(\text{[}\frac{X^2+1}{X^2-9}-\frac{X}{X+3}+\frac{5}{3-X}\text{]}\div\text{[}\frac{2X+10}{X+3}-1\text{]}\)1]
A ,RÚT GỌN P
B.TÍNH P KHI [X-1]=2
C.TÌM X ĐỂ P=\(\frac{X+5}{6}\)
Ai giải giúp mấy bài toán vs
Bài 1:
A=\(\sqrt{\frac{1}{\text{√}2+1}-\frac{\text{√}8-\text{√}10}{2-\text{√}5}}\)
B=\(\frac{5\text{√}5}{\text{√}5+2}+\frac{\text{√}5}{\text{√}5-1}-\frac{3\text{√}5}{3+\text{√}5}\)
Bài 2 rút gọn biểu thức
A=\(\left(\frac{x+\sqrt[]{xy}}{\text{√}x+\text{√}y}-2\right):\frac{1}{\text{√}x+2}\) với x :y >0
B=\(\left(\frac{a}{a-2\text{√}a}+\frac{a}{\text{√}a-2}\right):\frac{\text{√}a+1}{a-4\text{√}a+4}\)
Bài 3 cho biểu thức
P=\(\left(\frac{x-2}{x+2\text{√}x}+\frac{1}{\text{√}x+2}\right)\frac{\text{√}x+1}{\text{√}x-1}\)
a)Rút gọn P
b)tìm x để P=\(\text{√}x+\frac{5}{2}\)
bài 4 rút gọn biểu thức
A=\(\frac{1}{x+\text{√}x}+\frac{2\text{√}x}{x-1}-\frac{1}{x-\text{√}x}\)
B=\(\left(\frac{x}{x+3\text{√}x}+\frac{1}{\text{√}x+3}\right):\left(1-\frac{2}{\text{√}x}+\frac{6}{x+3\text{√}x}\right)\)
Bài 5
A=\(\left(\frac{2}{\text{√}x-3}-\frac{1}{\text{√}x+3}-\frac{x}{\text{√}x\left(x-9\right)}\right):\text{(√}x+3-\frac{x}{\text{√}x-3}\)
a)rút gọn A
b)tìm gtri x để A= -1/4
AI GIẢI GIÙM MÌNH ĐI MÌNH TẠ ƠN
Cho biểu thức
A= \(\text{[}1-\frac{\sqrt{x}}{1+\sqrt{x}}\text{]}:\text{[}\frac{\sqrt{x}+3}{\sqrt{x}+2}+\frac{\sqrt{x}+2}{3-\sqrt{x}}+\frac{\sqrt{x}+2}{x-5\sqrt{x}+6}\)
a, Rút gọn A
b, Tìm x để A<0
a: \(A=\dfrac{1}{\sqrt{x}+1}:\left(\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)
\(=\dfrac{1}{\sqrt{x}+1}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\)
\(=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\)
b: Để A<0 thì \(\sqrt{x}-2< 0\)
hay 0<x<4
Cho biểu thức
A=\(\text{[}1-\frac{\sqrt{x}}{1+\sqrt{x}}\text{]}:\text{[}\frac{\sqrt{x}+3}{\sqrt{x}-2}+\frac{\sqrt{x}+2}{3-\sqrt{x}}+\frac{\sqrt{x}+2}{x-5\sqrt{x}+6}\)
a, Rút gọn A
b, Tìm x để A= \(\frac{1}{2}\)
a) A= (\(\left(\frac{1+\sqrt{x}}{1+\sqrt{x}}-\frac{\sqrt{x}}{1+\sqrt{x}}\right):\left(\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x-2}\right)}+\frac{\sqrt{x}+2}{x-2\sqrt{x}-3\sqrt{x}+6}\right)\)
A=\(\left(\frac{1+\sqrt{x}-\sqrt{x}}{1+\sqrt{x}}\right):\left(\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}+\frac{\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}-2\right)-3\left(\sqrt{x}-2\right)}\right)\)
A= \(\left(\frac{1}{1+\sqrt{x}}\right):\left(\frac{x-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{x-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}+\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)
A=\(\left(\frac{1}{1+\sqrt{x}}\right):\left(\frac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)
A=\(\left(\frac{1}{1+\sqrt{x}}\right):\left(\frac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right)\)
A=\(\frac{\sqrt{x}-2}{\sqrt{x}+1}\)
b) Để A = \(\frac{1}{2}\)
thì \(\frac{\sqrt{x}-2}{\sqrt{x}+1}=\frac{1}{2}\)
=> 2\(\sqrt{x}-4\)=\(\sqrt{x}+1\)
=> \(\sqrt{x}=5\)
=> x = 25
Cho biểu thức
A=\(\orbr{ }\frac{x^2}{x^3-4x}+\frac{6}{6-3x}+\frac{1}{x+2}\text{] }\div\orbr{ }x-2+\frac{10-x^2}{x+2}\text{] }\)
a. Rút gọn A
b. Tìm giá trị của x để A có giá trị nguyên
\(A=\left[\frac{x^2}{x^3-4x}+\frac{6}{6-3x}+\frac{1}{x+2}\right]:\left[x-2+\frac{10-x^2}{x+2}\right]\) ĐKXĐ : \(x\ne0;x\ne\pm2\)
\(A=\left[\frac{x^2}{x\left(x+2\right)\left(x-2\right)}-\frac{6}{3\left(x-2\right)}+\frac{1}{x+2}\right]:\left[\frac{x^2-4}{x+2}+\frac{10-x^2}{x+2}\right]\)
\(A=\left[\frac{3x^2}{3x\left(x+2\right)\left(x-2\right)}-\frac{6x\left(x+2\right)}{3x\left(x+2\right)\left(x-2\right)}+\frac{3x\left(x+2\right)}{3x\left(x+2\right)\left(x-2\right)}\right]:\frac{6}{x+2}\)
\(A=\left[\frac{3x^2-6x^2-12x+3x^2+6x}{3x\left(x+2\right)\left(x-2\right)}\right].\frac{x+2}{6}\)
\(A=\frac{-x}{3x\left(x-2\right)}\)
\(A=\frac{-1}{3x-6}\)
Cho biểu thức
A= \(\text{[}\frac{x+1}{x-1}-\frac{x-1}{x+1}\text{]}:\text{[}\frac{2}{x^2-1}-\frac{x}{x-1}+\frac{1}{x+1}\text{]}\)
a, Rút gọn A
b, Tính giá trị của A khi x =\(\sqrt{3+\sqrt{8}}\)
c, Tìm x để A= \(\sqrt{5}\)
ĐKXĐ : \(x\ne\pm1\)
a/ \(A=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right):\left(\frac{2}{x^2-1}-\frac{x}{x-1}+\frac{1}{x+1}\right)\)
\(=\frac{x^2+2x+1-\left(x^2-2x+1\right)}{\left(x-1\right)\left(x+1\right)}:\frac{2-x\left(x+1\right)+\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\frac{4x}{\left(x-1\right)\left(x+1\right)}.\frac{\left(x-1\right)\left(x+1\right)}{1-x^2}=\frac{4x}{1-x^2}\)
b/ Ta có \(3+2\sqrt{2}=\left(\sqrt{2}+1\right)^2\Rightarrow\sqrt{3+\sqrt{8}}=\sqrt{2}+1\)
Suy ra : Nếu x = \(\sqrt{2}+1\) thì \(A=\frac{4\left(\sqrt{2}+1\right)}{1-\left(\sqrt{2}+1\right)^2}=\frac{4\left(\sqrt{2}+1\right)}{-\sqrt{2}.\sqrt{2}\left(\sqrt{2}+1\right)}=-\frac{4}{2}=-2\)
c/ \(A=\sqrt{5}\Rightarrow4x=\sqrt{5}\left(1-x^2\right)\Leftrightarrow\sqrt{5}x^2+4x-\sqrt{5}=0\)
Nhân cả hai vế của pt trên với \(\sqrt{5}\ne0\)
Được \(5x^2+4\sqrt{5}x-5=0\) . Đặt \(t=x\sqrt{5}\) pt trở thành \(t^2+4t-5=0\Leftrightarrow\left(t+5\right)\left(t-1\right)=0\) \(\Leftrightarrow\left[\begin{array}{nghiempt}t=1\\t=-5\end{array}\right.\)
Với t = 1 thì \(x=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}\)
Với t = -5 thì \(x=-\frac{5}{\sqrt{5}}=-\sqrt{5}\)
\(A=\left[\frac{x^2+2x+1-x^2+2x-1}{x^2-1}\right]:\left[\frac{2-x^2-x+x-1}{x^2-1}\right]=\left[\frac{4x}{x^2-1}\right].\left[\frac{x^2-1}{1-x^2}\right]=\frac{4x}{1-x^2}\)
Thực hiện phép tính
a) \(\frac{\text{x + 9}}{x^2 - 9}-\frac{\text{3}}{\text{x^2 + 3x}}\)
b) \(\frac{\text{3x + 5 }}{\text{x^2 - 5x }}+\frac{\text{ 25 - x }}{\text{25 - 5x }}\)
c) \(\frac{\text{3 }}{\text{2x }}+\frac{\text{3x - 3 }}{\text{2x - 1 }}+\frac{ 2x^2 + 1 }{\text{4x^2 - 2x }}\)
d) \(\frac{\text{1}}{\text{3x - 2 }}-\frac{1}{\text{3x + 2 }}- \frac{\text{3x - 6}}{\text{4 - 9x^2}}\)
e) \(\frac{\text{18 }}{\text{(x - 3)(x^2 - 9) }}-\frac{\text{3 }}{\text{x^2 - 6x + 9 }}-\frac{\text{x}}{\text{x^2 - 9}}\)
g) \(\frac{\text{x + 2 }}{\text{x + 3 }}-\frac{\text{5 }}{\text{x^2 + x - 6 }}+\frac{\text{1}}{\text{2 - x}}\)
h) \(\frac{\text{4x }}{\text{x + 2 }}-\frac{\text{3x }}{\text{x - 2 }}+\frac{\text{12x}}{\text{x^2 - 4}}\)
i) \(\frac{\text{ x + 1 }}{\text{ x - 1 }}-\frac{\text{ x - 1 }}{\text{ x + 1 }}-\frac{\text{4}}{\text{1 - x^2}}\)
k) \(\frac{\text{
3x + 21
}}{\text{
x^2 - 9
}}+\frac{\text{2 }}{\text{x + 3 }}-\frac{\text{3}}{\text{x - 3}}\)
cho P =
\(\frac{x^2+2\text{x}}{2\text{x}+10}\)+ \(\frac{x-5}{x}\)- \(\frac{6\text{x}+5}{\left(2\text{x}+3\right)\left(2\text{x}-3\right)}\)
a, Rút gọn
b, tìm x để P=1;P=-3
cho biểu thức\(A=\left(\frac{\text{x+1}}{\text{x-1}}-\frac{\text{x-1}}{\text{x+1}}+\frac{\text{x^2-4x-1)}}{\text{x^2-1}}\right)\div\frac{x}{x+2019}\)
a) tìm điều kiện xát định và rút gọn
b) với \(x\in z\)tìm GTLN của biểu thức
mik cần gấp câu b
A=1- (\(\text{ }\frac{\text{2x^2 - 1+x}}{\text{1-x^2}}\text{+}\text{ }\frac{\text{2x^3 - x +x^2}}{\text{1+x^2}}\)) * \(\frac{\text{(((1-x)(x^2-x)}}{\text{2x - 1}}\)
Rút gọn A và Cm A < 4/3