Thực hiện các phép tính sau:
\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}\);
K
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31 tháng 8 2020
\(\frac{5x+10}{4x-8}\cdot\frac{4-2x}{x+2}\)( ĐKXĐ : \(x\ne\pm2\))
\(=\frac{5\left(x+2\right)}{2\left(2x-4\right)}\cdot\frac{-\left(2x-4\right)}{x+2}\)
\(=\frac{-5\left(x+2\right)\left(2x-4\right)}{2\left(2x-4\right)\left(x+2\right)}\)
\(=-\frac{5}{2}\)
\(\frac{x^2-36}{2x+10}\cdot\frac{3}{6-x}\)( ĐKXĐ : \(x\ne-5;x\ne6\))
\(=\frac{\left(x-6\right)\left(x+6\right)}{2\left(x+5\right)}\cdot\frac{3}{-\left(x-6\right)}\)
\(=\frac{3\left(x-6\right)\left(x+6\right)}{-2\left(x+5\right)\left(x-6\right)}\)
\(=\frac{3\left(x+6\right)}{-2\left(x+5\right)}=\frac{3x+18}{-2x-10}=-\frac{3x+18}{2x+10}\)
31 tháng 8 2020
a)
Điều kiện : \(\hept{\begin{cases}4x-8\ne0\\x+2\ne0\end{cases}}\)
\(\hept{\begin{cases}x\ne2\\x\ne-2\end{cases}}\)
\(=\frac{5\left(x+2\right)}{-2\left(4-2x\right)}\cdot\frac{4-2x}{x+2}\)
\(=\frac{-5}{2}\)
b)
Điều kiện : \(\hept{\begin{cases}2x+10\ne0\\6-x\ne0\end{cases}}\)
\(\hept{\begin{cases}x\ne-5\\x\ne6\end{cases}}\)
\(=\frac{\left(x-6\right)\left(x+6\right)}{2x+10}\cdot\frac{3}{6-x}\)
\(=\frac{-6\left(x+6\right)\cdot3}{2x+10}\)
\(=\frac{-9\left(x+6\right)}{x+5}\)
\(=\frac{-9x-54}{x+5}\)
\(=\frac{-9\left(x+5\right)-9}{x+5}\)
\(=-9-\frac{9}{x+5}\)
15 tháng 12 2017
a) \(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}.\frac{2\left(2-x\right)}{x+2}=\frac{-5}{2}\)
b) \(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}=\frac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}.\frac{3x}{2\left(1-2x\right)}=\frac{3\left(1+2x\right)}{2\left(x+4\right)}=\frac{3+6x}{2x+8}\)
U
15 tháng 3 2020
1,\(\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x}{x\left(2x+6\right)}+\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x+x-6}{x\left(2x+6\right)}\)=\(\frac{4x-6}{x\left(2x+6\right)}=\frac{2\left(2x-3\right)}{x\left(2x+6\right)}\)
TH
1
26 tháng 6 2017
\(\frac{5x-5}{2x+2}:\frac{x^2-x}{2x^2+4x+2}\)
\(=\frac{5\left(x-1\right)}{2\left(x+1\right)}.\frac{2\left(x+1\right)^2}{x\left(x-1\right)}\)
\(=\frac{5\left(x+1\right)}{x}\)
27 tháng 3 2020
a) Ta có: \(\frac{x+1}{2x+6}+\frac{2x+3}{x^2+3x}\)
\(=\frac{x+1}{2\left(x+3\right)}+\frac{2x+3}{x\left(x+3\right)}\)
\(=\frac{x\left(x+1\right)}{2x\left(x+3\right)}+\frac{2\cdot\left(2x+3\right)}{2x\left(x+3\right)}\)
\(=\frac{x^2+x+4x+6}{2x\left(x+3\right)}\)
\(=\frac{x^2+5x+6}{2x\left(x+3\right)}\)
\(=\frac{x^2+2x+3x+6}{2x\left(x+3\right)}\)
\(=\frac{x\left(x+2\right)+3\left(x+2\right)}{2x\left(x+3\right)}\)
\(=\frac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\frac{x+2}{2x}\)
b) Ta có: \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
\(=\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
\(=\frac{3x}{x\left(2x+6\right)}-\frac{x-6}{x\left(2x+6\right)}\)
\(=\frac{3x-x+6}{x\left(2x+6\right)}=\frac{2x+6}{x\left(2x+6\right)}=\frac{1}{x}\)
c) Ta có: \(\frac{5x+10}{4x-8}\cdot\frac{4-2x}{x+2}\)
\(=\frac{5\left(x+2\right)\cdot2\cdot\left(2-x\right)}{4\cdot\left(x-2\right)\cdot\left(x+2\right)}\)
\(=\frac{5\cdot2\cdot\left(2-x\right)}{-4\left(2-x\right)}=\frac{5\cdot2}{-4}=\frac{-5}{2}\)
d) Ta có: \(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
\(=\frac{\left(1-2x\right)\left(1+2x\right)\cdot3x}{x\left(x+4\right)\cdot2\left(2-x\right)}\)
\(=\frac{\left(1-2x\right)\left(1+2x\right)\cdot3}{2\left(x+4\right)\cdot\left(2-x\right)}=\frac{3\left(1-4x^2\right)}{2\left(-x^2-2x+8\right)}\)
\(=\frac{3-12x^2}{-2x^2-4x+16}\)
JS
27 tháng 3 2020
a) \(\frac{x+1}{2x+6}+\frac{2x+3}{x^2+3x}\)
\(=\frac{x+1}{2\left(x+3\right)}+\frac{2x+3}{x\left(x+3\right)}\) \(\left(ĐKXĐ:x\ne-3;x\ne0\right)\)
\(=\frac{x^2+x}{2x\left(x+3\right)}+\frac{4x+6}{2x\left(x+3\right)}\)
\(=\frac{x^2+2x+3x+6}{2x\left(x+3\right)}=\frac{\left(x+2\right)\left(x+3\right)}{2x\left(x+3\right)}=\frac{x+2}{2x}\)
b) \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\) \(\left(ĐKXĐ:x\ne0;x\ne-3\right)\)
\(=\frac{3x}{2x\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}=\frac{2\left(x+3\right)}{2x\left(x+3\right)}=\frac{1}{x}\)
c) \(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}.\frac{2\left(2-x\right)}{x+2}\) \(\left(ĐKXĐ:x\ne\pm2\right)\)
\(=\frac{-5\left(x-2\right)}{2\left(x-2\right)}=\frac{-5}{2}\)
ET
4 tháng 12 2018
a) \(\dfrac{5x+10}{4x-8}.\dfrac{4-2x}{x+2}\\ =\dfrac{-5x-10}{8-4x}.\dfrac{4-2x}{x+2}\\ =\dfrac{-5\left(x+2\right)}{4\left(2-x\right)}.\dfrac{2\left(2-x\right)}{x+2}=\dfrac{-5}{2}\)
b)\(\dfrac{x^2-36}{2x+10}.\dfrac{3}{6-x}\\ =\dfrac{\left(x-6\right).\left(x+6\right)}{2\left(x+5\right)}.\dfrac{-3}{x-6}\\ =\dfrac{-3x-18}{2x+10}\)
HQ
Hà Quang Minh
Giáo viên
20 tháng 9 2023
\(\frac{{9{x^2} + 5x + x}}{{3x}} = \frac{{9{x^2} + 6x}}{{3x}} = \frac{{9{x^2}}}{{3x}} + \frac{{6x}}{{3x}} = 3x + 2\)
\(\frac{{2{x^2} - 3x - 2}}{{2 - x}} = \frac{{2{x^2} - 3x - 2}}{{ - x + 2}} = - 2x - 1\)
TT
1
\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{\left(5x+10\right).\left(4-2x\right)}{\left(4x-8\right).\left(x+2\right)}\)
\(=\frac{5\left(x+2\right).2\left(2-x\right)}{4\left(x-2\right)\left(x+2\right)}\)
\(=\frac{5\left(2-x\right)}{2\left(x-2\right)}=-\frac{5}{2}\)
\(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{\left(5x+10\right)\left(4-2x\right)}{\left(4x-8\right)\left(x+2\right)}\\ =\frac{5\left(x+2\right).2\left(2-x\right)}{4\left(x-2\right)\left(x+2\right)}\\ =\frac{5\left(2-x\right)}{2\left(x-2\right)}=-\frac{5}{2}\)