# Bài 6: Phép trừ các phân thức đại số

22 tháng 12 2020 lúc 22:49

a) Ta có: $\dfrac{9-3x}{x^2+3x+4}-\dfrac{3x-23}{\left(1-x\right)\left(x+4\right)}$

$=\dfrac{9-3x}{x^2+3x+4}+\dfrac{3x-23}{x^2+3x-4}$

$=\dfrac{\left(9-3x\right)\left(x^2+3x-4\right)}{\left(x^2+3x+4\right)\left(x^2+3x-4\right)}+\dfrac{\left(3x-23\right)\left(x^2+3x+4\right)}{\left(x^2+3x-4\right)\left(x^2+3x+4\right)}$

$=\dfrac{9x^2+27x-36-3x^3-9x^2+12x+3x^3+9x^2+12x-23x^2-69x-92}{\left(x^2+3x-4\right)\left(x^2+3x+4\right)}$

$=\dfrac{-14x^2-18x-128}{\left(x^2+3x-4\right)\left(x^2+3x+4\right)}$

b) Ta có: $\dfrac{4-x}{x^3+2x}-\dfrac{x+5}{x^3-x^2+2x-2}$

$=\dfrac{4-x}{x\left(x^2+2\right)}-\dfrac{x+5}{x^2\left(x-1\right)+2\left(x-1\right)}$

$=\dfrac{4-x}{x\left(x^2+2\right)}-\dfrac{x+5}{\left(x-1\right)\left(x^2+2\right)}$

$=\dfrac{\left(4-x\right)\left(x-1\right)}{x\left(x-1\right)\left(x^2+2\right)}-\dfrac{x\left(x+5\right)}{x\left(x-1\right)\left(x^2+2\right)}$

$=\dfrac{4x-4-x^2+x-x^2-5x}{x\left(x-1\right)\left(x^2+2\right)}$

$=\dfrac{-2x^2-4}{x\left(x-1\right)\left(x^2+2\right)}$

$=\dfrac{-2\left(x^2+2\right)}{x\left(x-1\right)\left(x^2+2\right)}$

$=\dfrac{-2}{x\left(x-1\right)}$

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17 tháng 12 2020 lúc 22:04

Ta có: $A=\dfrac{a^2}{\left(a-b\right)\left(a-c\right)}-\dfrac{b^2}{\left(b-a\right)\left(c-b\right)}-\dfrac{c^2}{\left(c-a\right)\left(b-c\right)}$

$=\dfrac{a^2\left(b-c\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}-\dfrac{b^2\left(a-c\right)}{\left(a-b\right)\left(b-c\right)\left(a-c\right)}+\dfrac{c^2\left(a-b\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}$

$=\dfrac{a^2b-a^2c-ab^2+b^2c+ac^2-bc^2}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}$

$=\dfrac{ab\left(a-b\right)-c\left(a^2-b^2\right)+c^2\left(a-b\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}$

$=\dfrac{\left(a-b\right)\left(ab+c^2\right)-c\left(a-b\right)\left(a+b\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}$

$=\dfrac{\left(a-b\right)\left(ab+c^2-c\right)}{\left(a-b\right)\left(a-c\right)\left(b-c\right)}$

$=\dfrac{c^2+ab-c}{\left(a-c\right)\left(b-c\right)}$

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17 tháng 12 2020 lúc 11:06

MTC = (x - y)(x2 + xy + y2)

$\dfrac{1}{x-y}-\dfrac{3xy}{x^3-y^3}+\dfrac{x-y}{x^2+xy+y^2}$

$=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{x^2+xy+y^2-3xy+\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}$

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16 tháng 12 2020 lúc 22:19

1/x-y-3xy/x^3-y^3+x-y/x^2+xy+y^2

=1/x-y+-3xy/(x-y)(x^2+xy+y^2)+x-y/x^2+xy+y^2

=x^2+xy+y^2/(x-y)(x^2+xy+y^2)+-3xy/(x-y)(x^2+xy+y^2)+x^2-2xy+y^2/(x-y)(x^2+xy+y^2)

=x^2+xy+y^2-3xy+x^2-2xy-y^2/(x-y)(x^2+xy+y^2)

=2x^2-5xy/(x-y)(x^2+xy+y^2)

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17 tháng 12 2020 lúc 11:06

MTC = (x - y)(x2 + xy + y2)

$\dfrac{1}{x-y}-\dfrac{3xy}{x^3-y^3}+\dfrac{x-y}{x^2+xy+y^2}$

$=\dfrac{x^2+xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{x^2+xy+y^2-3xy+\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x^2-2xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}$

$=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}$

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13 tháng 12 2020 lúc 21:27

Ta có: $\dfrac{-4x^2}{x^2-25}-\dfrac{2x^2+x}{x^2-25}-\dfrac{2x}{5-x}$

$=\dfrac{-4x^2-2x^2-x}{\left(x-5\right)\left(x+5\right)}+\dfrac{2x}{x-5}$

$=\dfrac{-6x^2-x}{\left(x-5\right)\left(x+5\right)}+\dfrac{2x\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}$

$=\dfrac{-6x^2-x+2x^2+10x}{\left(x-5\right)\left(x+5\right)}$

$=\dfrac{-4x^2+9x}{\left(x-5\right)\left(x+5\right)}$

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13 tháng 12 2020 lúc 21:35

$\dfrac{-4+25}{x^2-25}-\dfrac{2x^2+x}{x^2-25}-\dfrac{2x}{5-x}$

= $\dfrac{-4+25}{x^2-25}-\dfrac{2x^2+x}{x^2-25}+\dfrac{2x\left(x+5\right)}{x^2-25}$

= $\dfrac{-4+25-2x^2-x+2x^2+10x}{x^2-25}$

= $\dfrac{21+9x}{x^2-25}$

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7 tháng 12 2020 lúc 21:19

Ta có: $\frac{x^2+y^2}{\left(x-y\right)^3}-\frac{2xy}{\left(x-y\right)^3}$

$=\frac{x^2-2xy+y^2}{\left(x-y\right)^3}$

$=\frac{\left(x-y\right)^2}{\left(x-y\right)^3}=\frac{1}{x-y}$

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3 tháng 5 2020 lúc 9:19

Ta có: $\frac{3x+2}{\left(x-1\right)^2}-\frac{6}{x^2-1}-\frac{3x-2}{x^2+2x+1}$

$=\frac{\left(3x+2\right)\cdot\left(x+1\right)^2}{\left(x-1\right)^2\cdot\left(x+1\right)^2}-\frac{6\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2\cdot\left(x+1\right)^2}-\frac{\left(3x-2\right)\left(x-1\right)^2}{\left(x+1\right)^2\cdot\left(x-1\right)^2}$

$=\frac{3x^3+8x^2+7x+2-6x^2+6-3x^3+8x^2-7x+2}{\left(x^2-1\right)^2}$

$=\frac{10x^2+10}{\left(x^2-1\right)^2}$

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2 tháng 3 2020 lúc 15:09
https://i.imgur.com/qz7eYvL.jpg
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2 tháng 3 2020 lúc 15:12

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. $\frac{4x-1}{3x^2y}-\frac{7x-1}{3x^2y}=\frac{4x-1-7x+1}{3x^2y}=\frac{-3x}{3x^2y}=\frac{-1}{xy}$

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