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1,\(\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x}{x\left(2x+6\right)}+\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x+x-6}{x\left(2x+6\right)}\)=\(\frac{4x-6}{x\left(2x+6\right)}=\frac{2\left(2x-3\right)}{x\left(2x+6\right)}\)
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: \(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
\(=\frac{\left(1-2x\right)\left(1+2x\right)\cdot3x}{x\left(x+4\right)\cdot2\left(2-x\right)}\)
\(=\frac{\left(1-2x\right)\left(1+2x\right)\cdot3}{2\left(x+4\right)\cdot\left(2-x\right)}=\frac{3\left(1-4x^2\right)}{2\left(-x^2-2x+8\right)}\)
\(=\frac{3-12x^2}{-2x^2-4x+16}\)
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) \(\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}.\frac{2\left(2-x\right)}{x+2}\) \(\left(ĐKXĐ:x\ne\pm2\right)\)
\(=\frac{-5\left(x-2\right)}{2\left(x-2\right)}=\frac{-5}{2}\)
\(1,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}=\frac{3}{2x+6}-\frac{x-6}{x\left(2x-6\right)}=\frac{3x-x+6}{x\left(2x-6\right)}=\frac{2x+6}{x\left(2x-6\right)}\)
\(2,\frac{1}{1-x}+\frac{2x}{x^2-1}=\frac{-1\left(x+1\right)+2x}{x^2-1}=\frac{x-1}{x^2-1}=\frac{1}{x+1}\)
\(3,\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)
\(4,\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}.\frac{2\left(2-x\right)}{x+2}=\frac{-5}{2}\)
\(5,\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}=\frac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}.\frac{3x}{2\left(1-2x\right)}=\frac{3\left(1+2x\right)}{2x\left(x+4\right)}\)
\(6,\frac{12x}{5y^3}.\frac{15y^4}{8x^3}=\frac{9y}{2x^2}\)
\(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x^2+x}\)
b, \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{y^2-xy-xy+x^2}{\left(xy-x^2\right)\left(y^2-xy\right)}=\frac{x^2+y^2}{xy^3-xyxy-xyxy+x^3y}\)Tu rut gon tiep
c, tt
d, cx r
a) \(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}\)
\(=\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{x\left(x+1\right)}\)
b) \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)
\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)
c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}=\frac{9x-3}{4x-1}+\frac{3x}{4x-1}\)
\(=\frac{9x-3+3x}{4x-1}=\frac{6x-3}{4x-1}\)
\(\frac{x^2-3x-x+3}{x-3}=\frac{x\left(x-3\right)-\left(x-3\right)}{x-3}=\frac{\left(x-3\right)\left(x-1\right)}{x-3}=x-1\)( ĐK: \(x\ne3\))
\(\frac{2x^3-5x^2-4x+3}{2x-1}=\frac{\left(2x^3-x^2\right)-\left(4x^2-2x\right)-\left(6x-3\right)}{2x-1}=\frac{x^2\left(2x-1\right)-2x\left(2x-1\right)-3\left(2x-1\right)}{2x-1}=\frac{\left(2x-1\right)\left(x^2-2x-3\right)}{2x-1}=x^2-2x-3\)( ĐK: \(x\ne\frac{1}{2}\))
Tham khảo nhé~
a) \(\frac{3x+5}{2\left(x-1\right)}+\frac{4}{x-2}=\frac{\left(3x+5\right)\left(x-2\right)+4\cdot2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)}=\frac{3x^2-6x+5x-10+8x-8}{2\left(x-1\right)\left(x-2\right)}\)
\(=\frac{3x^2+7x-18}{2\left(x-1\right)\left(x-2\right)}\)
b) \(\frac{2x^2+1}{4x^2-2x}+\frac{3-3x}{1-2x}+\frac{3}{2x}=\frac{2x^2+1+4x\left(3-3x\right)+2\cdot3\left(1-2x\right)}{4x\left(1-2x\right)}=\frac{2x^2+1+12-12x+6-12x}{4x\left(1-2x\right)}\)\(=\frac{2x^2-24x+19}{4x\left(1-2x\right)}\)
Đề này... bạn xem lại đi. Chứ thế này thì dùng máy tính cũng không làm nổi T-T
\( a)\dfrac{{3{x^4} - 2{x^3} - 2{x^2} + 4x - 8}}{{{x^2} - 2}}\\ = \dfrac{{3{x^4} - 2{x^3} - 6{x^2} + 4{x^2} + 4x - 8}}{{{x^2} - 2}}\\ = \dfrac{{3{x^2}\left( {{x^2} - 2} \right) - 2x\left( {{x^2} - 2} \right) + 4\left( {{x^2} - 2} \right)}}{{{x^2} - 2}}\\ = \dfrac{{\left( {{x^2} - 2} \right)\left( {3{x^2} - 2x + 4} \right)}}{{{x^2} - 2}}\\ = 3{x^2} - 2x + 4 \)
\( b)\dfrac{{2{x^3} - 26x - 24}}{{{x^2} + 4x + 3}}\\ = \dfrac{{2\left( {{x^3} - 13x - 12} \right)}}{{x + 3x + x + 3}}\\ = \dfrac{{2\left( {{x^3} + {x^2} - {x^2} - x - 12x - 12} \right)}}{{x\left( {x + 3} \right) + x + 3}}\\ = \dfrac{{2\left[ {{x^2}\left( {x + 1} \right) - x\left( {x + 1} \right) - 12\left( {x + 1} \right)} \right]}}{{\left( {x + 3} \right)\left( {x + 1} \right)}}\\ = \dfrac{{2\left( {x + 1} \right)\left( {{x^2} - x - 12} \right)}}{{\left( {x + 3} \right)\left( {x + 1} \right)}}\\ = \dfrac{{2\left( {{x^2} + 3x - 4x - 12} \right)}}{{x + 3}}\\ = \dfrac{{2\left[ {x\left( {x + 3} \right) - 4\left( {x + 3} \right)} \right]}}{{x + 3}}\\ = \dfrac{{2\left( {x + 3} \right)\left( {x - 4} \right)}}{{x + 3}}\\ = 2\left( {x - 4} \right)\\ = 2x - 8\)
P/s : Phá ngoặc ra là ok :
a )
\(\left[4x-2\left(x-3\right)\right].\left(-3x\right)\)
\(=\left[4x-2x+6\right]\left(-3x\right)\)
\(=-12x^2+6x^2-18x\)
b )
\(3\left[x-3\left(4-2x\right)+8\right]\)
\(=3\left[x-12+6x+8\right]\)
\(=3\left[7x-4\right]\)
\(=21x-12\)
c )
\(5\left(3x^2-4y^3\right)+9\left(2x^2-y^3\right)\)
\(=15x^2-20y^3+18x^2-9y^3\)
\(=33x^2-29y^3\)
d )
\(3x^2\left(2y-1\right)-2x^2\left(5y-3\right)\)
\(=6x^2y-3x^2-10x^2y+6x^2\)
\(=-4x^2y+3x^2\)