\(\frac{3x+1}{7x^2y}+\frac{2x+2}{7x^2y}\)
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AH
Akai Haruma
Giáo viên
4 tháng 1 2020
Lời giải:
\(\frac{5xy-4y}{2x^2y^3}+\frac{3xy-4y}{2x^2y^3}=\frac{8xy-8y}{2x^2y^3}=\frac{8y(x-1)}{2x^2y^3}=\frac{4(x-1)}{x^2y^2}\)
\(\frac{4x-1}{3x^2y}-\frac{7x-1}{3x^2y}=\frac{-3x}{3x^2y}=\frac{-1}{xy}\)
26 tháng 12 2020
a. 2x(x + y) - y(y + 2x) = 2x2 + 2xy - y2 - 2xy = 2x2 - y2
b.\(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
Phần c nản quá.
XO
25 tháng 12 2020
a) 2x(x + y) - y(y + 2x)
= 2x2 + 2xy - y2 - 2xy
= 2x2 - y2
b) \(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
c) \(\frac{x^3-4x^2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{x-1}\)
= \(\frac{x^3-4x^2}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2\left(x-1\right)}{\left(x^2+x+1\right)\left(x-1\right)}+\frac{x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}\)
= \(\frac{x^3-4x^2+2x-2+x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{x^3-3x^2+3x-1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{\left(x-1\right)^3}{\left(x^2+x+1\right)\left(x-1\right)}\)
\(=\frac{\left(x-1\right)^2}{x^2+x+1}\)
6 tháng 1 2018
a.\(\frac{4x-1}{2x^2y}-\frac{7x-1}{3x^2y}\) MTC=6x2y
\(=\frac{3\left(4x-1\right)}{6x^2y}-\frac{2\left(7x-1\right)}{6x^2y}\)
\(=\frac{12x-3-\left(14x-2\right)}{6x^2y}\)
\(=\frac{12x-3-14x+2}{6x^2y}\)
\(=\frac{-2x-1}{6x^2y}=\frac{2\left(-x-1\right)}{6x^2y}=-\frac{x-1}{3x^2y}\)
b.\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\) MTC= 2x (x + 3)
\(=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\)
\(=\frac{3x}{2x\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}=\frac{3x-\left(x-6\right)}{2x\left(x+3\right)}\)
\(=\frac{3x-x+6}{2x\left(x+3\right)}=\frac{2x+6}{2x\left(x+3\right)}=\frac{2\left(x+3\right)}{2x\left(x+3\right)}=\frac{1}{x}\)
c.\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
\(=\frac{2x}{x\left(x+2y\right)}+\frac{y}{y\left(x-2y\right)}+\frac{4}{\left(x-2y\right)\left(x+2y\right)}\)MTC= xy (x+2y).(x-2y)
\(=\frac{2xy\left(x-2y\right)}{xy\left(x+2y\right)\left(x-2y\right)}+\frac{xy\left(x+2y\right)}{xy\left(x+2y\right)\left(x-2y\right)}+\frac{4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\frac{2x^2y-4xy^2+x^2y+2xy^2+4xy}{xy\left(x+2y\right)\left(x-2y\right)}\)
\(=\frac{3x^2y-2xy^2+4xy}{xy\left(x-2y\right)\left(x+2y\right)}=\frac{xy\left(3x-2y+4\right)}{xy\left(x-2y\right)\left(x+2y\right)}=\frac{3x-2y+4}{\left(x-2y\right)\left(x+2y\right)}\)
Chọn mk nha!
BL
2 tháng 3 2020
a.\(\frac{1-3x}{2}-\frac{x+3}{2}=\frac{1-3x-x-3}{2}=\frac{1-4x-3}{2}=\frac{-4x-2}{2}=\frac{-2\left(2x+1\right)}{2}=-2x-1\)
b. \(\frac{2\left(x+y\right)\left(x-y\right)}{x}-\frac{-2y^2}{x}=\frac{2\left(x^2-y^2\right)+2y^2}{x}=\frac{2x^2-2y^2+2y^2}{x}=2x\)
c. \(\frac{3x+1}{x+y}-\frac{2x-3}{x+y}=\frac{3x+1-2x+3}{x+y}=\frac{x+4}{x+y}\)
d. \(\frac{xy}{2x-y}-\frac{x^2-1}{y-2x}=\frac{xy}{2x-y}-\frac{1-x^2}{2x-y}=\frac{xy-1+x^2}{2x-y}\)
e. \(\frac{4x-1}{3x^2y}-\frac{7x-1}{3x^2y}=\frac{4x-1-7x+1}{3x^2y}=\frac{-3x}{3x^2y}=\frac{-1}{xy}\)
HT
23 tháng 8 2016
ĐKXĐ: \(x>-1;y\ge\frac{2}{9}\)
(2) \(\Leftrightarrow\left(x+1\right)-3\sqrt{x+1}-\frac{1}{\sqrt{x+1}}=y^2-3y-\frac{1}{y}\)
Xét \(f\left(t\right)=t^2-3t-\frac{1}{t};t>0\)
\(f'\left(t\right)=2t-3+\frac{1}{t^2}=\frac{2t^3-3t^2+1}{t^2}=\frac{\left(t-1\right)^2\left(2t+1\right)}{t^2}>0;\forall t>0\)
→ f(t) đồng biến trên (0;+∞)
Mà \(f\left(\sqrt{x+1}\right)=f\left(y\right)\Leftrightarrow\sqrt{x+1}=y\Leftrightarrow x=y^2-1\)
thế vào (1) ta được
\(\sqrt{9y-2}+\sqrt[3]{7y^2+2y-5}=2y+3\)
\(\Leftrightarrow\sqrt{9y-2}-\left(y+2\right)+\sqrt[3]{7y^2+2y-5}-\left(y+1\right)=0\)
\(\Leftrightarrow\frac{y^2-5y+6}{\sqrt{9y-2}+y+2}+\frac{y^3-4y^2+y+6}{\sqrt[3]{\left(7y^2+2y-5\right)^2}+\left(y+1\right)\sqrt[3]{7y^2+2y-5}+\left(y+1\right)^2}=0\)
\(\Leftrightarrow\left(y^2-5y+6\right)\left(\frac{1}{\sqrt{9y-2}+y+2}+\frac{y+1}{\sqrt[3]{\left(7y^2+2y-5\right)^2}+\left(y+1\right)\sqrt[3]{7y^2+2y-5}+\left(y+1\right)^2}\right)=0\)
\(\Leftrightarrow y^2-5y+6=0\Leftrightarrow\left[\begin{array}{nghiempt}y=2\Rightarrow x=3\\y=3\Rightarrow x=8\end{array}\right.\)
Vậy hệ đã cho có hai nghiệm (8;3) và (3;2)
bài này k phải toán lớp 5. nhưng mk sẽ giải giúp bạn.
\(=\frac{3x+1+2x+2}{7x^2y}=\frac{5x+3}{7x^2y}\)