\(\dfrac{2a+9}{9-4a}+\dfrac{-1}{2a+3}\)

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26 tháng 11 2017

a) \(\dfrac{2a+9}{9-4a^2}+\dfrac{-1}{2a+3}\)( sửa đề )

\(=\dfrac{-2a-9}{\left(2a+3\right)\left(2a-3\right)}-\dfrac{1}{2a+3}=\dfrac{-2a-9-2a+3}{\left(2a+3\right)\left(2a-3\right)}\)

\(=\dfrac{-4a-6}{\left(2a-3\right)\left(2a+3\right)}=\dfrac{-2\left(2a+3\right)}{\left(2a-3\right)\left(2a+3\right)}=\dfrac{-2}{2a-3}\)

30 tháng 7 2018

e) = \(\dfrac{3}{2\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\)

= \(\dfrac{3x}{2x\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\) = \(\dfrac{3x-x+6}{2x\left(x+3\right)}\)

= \(\dfrac{2x-6}{2x\left(x+3\right)}\)

= \(\dfrac{2\left(x-3\right)}{2x\left(x+3\right)}\)

30 tháng 7 2018

c) = \(\dfrac{2\left(a^3-b^3\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)

= \(\dfrac{-2\left(a+b\right)\left(a^2-2ab+b^2\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)

= \(\dfrac{-2\left(a+b\right)}{1}\) . \(\dfrac{2}{1}\) = -4 (a+b)

\(A=\left(\dfrac{-\left(2a-1\right)}{2a+1}+\dfrac{\left(2a-1\right)^2}{2a+1}\cdot\dfrac{1}{\left(2a-1\right)\left(2a+1\right)}\right)\cdot\left(\dfrac{4a\left(a+1\right)+1}{4a^2}\right)-\dfrac{1}{2a}\)

\(=\left(\dfrac{-\left(2a-1\right)}{2a+1}+\dfrac{2a-1}{\left(2a+1\right)^2}\right)\cdot\dfrac{4a^2+4a+1}{4a^2}-\dfrac{1}{2a}\)

\(=\dfrac{-\left(2a-1\right)\left(2a+1\right)}{\left(2a+1\right)^2}\cdot\dfrac{\left(2a+1\right)^2}{4a^2}-\dfrac{1}{2a}\)

\(=\dfrac{-\left(4a^2-1\right)}{4a^2}-\dfrac{2a}{4a^2}\)

\(=\dfrac{-4a^2-2a+1}{4a^2}\)

1: \(\Leftrightarrow\left(x+2\right)\left(x-2\right)+3\left(x+1\right)=3+x^2-x-2\)

\(\Leftrightarrow x^2-x+1=x^2-4+3x+3=x^2+3x-1\)

=>-4x=-2

hay x=1/2

2: \(\Leftrightarrow\left(x+6\right)^2+\left(x-5\right)^2=2x^2+23x+61\)

\(\Leftrightarrow x^2+12x+36+x^2-10x+25=2x^2+23x+61\)

\(\Leftrightarrow2x^2+23x+61=2x^2+2x+11\)

=>21x=-50

hay x=-50/21

3: \(\Leftrightarrow6\left(x-8\right)+\left(x+2\right)\left(x-5\right)=-18-\left(x-5\right)\left(x-8\right)\)

\(\Leftrightarrow6x-48+x^2-3x-10+18+x^2-13x+40=0\)

\(\Leftrightarrow2x^2-10x=0\)

=>2x(x-5)=0

=>x=0(nhận) hoặc x=5(loại)

\(=\left(\dfrac{2}{2a-b}-\dfrac{6b}{\left(2a-b\right)\left(2a+b\right)}-\dfrac{4}{2a+b}\right):\dfrac{4a^2-b^2+4a^2+b^2}{4a^2-b^2}\)

\(=\dfrac{4a+2b-6b-8a+4b}{\left(2a-b\right)\left(2a+b\right)}\cdot\dfrac{\left(2a-b\right)\left(2a+b\right)}{8a^2}\)

\(=\dfrac{-4a}{8a^2}=\dfrac{-1}{2a}\)

15 tháng 7 2017

cái này chỉ rút rọn được thôi

\(=\left(\dfrac{2\left(2a+b\right)-6b-4\left(2a-b\right)}{\left(2a-b\right)\left(2a+b\right)}\right):\dfrac{4a^2-b^2+4a^2+b^2}{\left(2a-b\right)\left(2a+b\right)}\)

\(=\dfrac{4a+2b-6b-8a+4b}{8a^2}\)

\(=\dfrac{-4a}{8a^2}=\dfrac{-1}{2a}\)

28 tháng 11 2022

a: \(=\dfrac{4a^2-4a+1-4a^2-2a+6a+3}{\left(2a-1\right)\left(2a+1\right)}\)

\(=\dfrac{4}{\left(2a-1\right)\left(2a+1\right)}\)

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

d: \(=\dfrac{x-5+6x}{x\left(x+3\right)}=\dfrac{7x-5}{x\left(x+3\right)}\)

e: \(=\dfrac{x^2-4+3}{x-2}=\dfrac{x^2-1}{x-2}\)

i: \(=\dfrac{x}{x\left(x-4\right)}-\dfrac{3}{5x}=\dfrac{1}{x-4}-\dfrac{3}{5x}\)

\(=\dfrac{5x-3x+12}{5x\left(x-4\right)}=\dfrac{2x+12}{5x\left(x-4\right)}\)