Qui đồng mẫu thức các phân thức:
\(\dfrac{-3}{x^2+6x+8};\dfrac{5}{x^2-16}\) và \(\dfrac{1}{x^2-2x-8}\)
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20 tháng 11 2018
\(\frac{1}{6x^2y^3}=\frac{7x^2}{42x^4y^3},\frac{-5}{21xy^2}=\frac{-10x^3y}{42x^4y^3},\frac{3}{14x^4y}=\frac{3y^2}{14x^4y^3}\)
21 tháng 11 2022
MTC=(x+2)(x+4)(x-2)(x-4)
\(\dfrac{-3}{x^2+6x+8}=\dfrac{-3\left(x-2\right)\left(x-4\right)}{\left(x+2\right)\left(x-2\right)\left(x+4\right)\left(x-4\right)}\)
\(\dfrac{5}{x^2-16}=\dfrac{5\left(x+2\right)\left(x-2\right)}{\left(x-4\right)\left(x+4\right)\left(x-2\right)\left(x+2\right)}\)
\(\dfrac{1}{x^2-2x-8}=\dfrac{1}{\left(x-4\right)\left(x+2\right)}=\dfrac{\left(x+4\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)\left(x+4\right)\left(x-4\right)}\)
CC
1
21 tháng 11 2018
Ta có \(\frac{2}{x^3-y^3}=\frac{2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(\frac{2x-1}{x^2-y^2}=\frac{2x+1}{\left(x+y\right)\left(x-y\right)}\)
\(\frac{1}{x+y}\) giữ nguyên
MTC: \(\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
Các nhân tử phụ tương ứng là : \(\left(x+y\right);\left(x-y\right)\left(x^2+xy+y^2\right);\left(x^2+xy+y^2\right)\)
Ta có:
\(\frac{2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\frac{2.\left(x+y\right)}{\left(x-y\right)\left(x+y\right)\left(x^2+xy+y^2\right)}\)
\(\frac{1}{x+y}=\frac{1.\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(\frac{2x+1}{\left(x+y\right)\left(x-y\right)}=\frac{\left(2x+1\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)}\)
CC
0
NT
1
20 tháng 11 2018
\(\frac{x+2}{4x-x^2-3}=\frac{-\left(x+2\right)}{x^2-4x+3}=\frac{\left(-x-2\right)\left(2x+5\right)}{\left(x-1\right)\left(x-3\right)\left(2x+5\right)}=\frac{-2x^2-9x-10}{\left(x-1\right)\left(x-3\right)\left(2x+5\right)}\)
\(\frac{1}{2x^2+3x-5}=\frac{1}{\left(x-1\right)\left(2x+5\right)}=\frac{x-3}{\left(x-1\right)\left(x-3\right)\left(2x+5\right)}\)
17 tháng 2 2021
a) MTC: \(12x^3y^3\)
\(\dfrac{3}{4x^3y^2}=\dfrac{3\cdot3y}{4x^3y^2\cdot3y}=\dfrac{9y}{12x^3y^3}\)
\(\dfrac{2}{3xy^3}=\dfrac{2\cdot4x^2}{3xy^3\cdot4x^2}=\dfrac{8x^2}{12x^3y^3}\)
b) MTC: \(x\left(x-3\right)^2\)
\(\dfrac{5}{x^2-6x+9}=\dfrac{5}{\left(x-3\right)^2}=\dfrac{5x}{x\left(x-3\right)^2}\)
\(\dfrac{3}{x^2-3x}=\dfrac{3}{x\left(x-3\right)}=\dfrac{3\left(x-3\right)}{x\left(x-3\right)^2}=\dfrac{3x-9}{x\left(x-3\right)^2}\)
CC
1
20 tháng 11 2018
\(\frac{4}{x^2-9}=\frac{4}{\left(x-3\right)\left(x+3\right)}=\frac{4x}{x\left(x-3\right)\left(x+3\right)}\)
\(\frac{1-x}{3x-x^2}=\frac{x-1}{x^2-3x}=\frac{\left(x-1\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)}\)
\(\frac{-3}{x^2+6x+8}=\frac{-3}{x\left(x+2\right)+4\left(x+2\right)}=\frac{-3}{\left(x+2\right)\left(x+4\right)}=\frac{-3x+12}{\left(x+2\right)\left(x+4\right)\left(x-4\right)}\)
\(\frac{5}{x^2-16}=\frac{5}{\left(x-4\right)\left(x+4\right)}=\frac{5x+10}{\left(x+2\right)\left(x-4\right)\left(x+4\right)}\)
\(\frac{1}{x^2-2x-8}=\frac{1}{x\left(x-4\right)+2\left(x-4\right)}=\frac{1}{\left(x-4\right)\left(x+2\right)}=\frac{x+4}{\left(x+2\right)\left(x+4\right)\left(x-4\right)}\)