Cho \(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4+16}\right).\dfrac{a^4x^4+16}{a^4x^4}\)
a. Rút gọn
b. tìm P biết \(\dfrac{a^2+4}{x^2+9}=\dfrac{a^2}{9}\)
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AT
2 tháng 4 2018
\(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^2x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{ax+2+ax-2}{a^2x^2-4}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{2ax\left(a^2x^2+4\right)+2ax\left(a^2x^2-4\right)}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{4a^3x^3}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\dfrac{8a^7x^7-64a^3x^3}{a^4x^4\left(a^4x^4-16\right)}\cdot\dfrac{a^4x^4+16}{a^4x^4}=\dfrac{\left(8a^7x^7-64a^3x^3\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}\)
\(=\dfrac{8a^3x^3\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}=\dfrac{8\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^5x^5\left(a^4x^4-16\right)}\)
26 tháng 12 2021
\(a,A=\dfrac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}=\dfrac{4}{x+4}\\ b,B=\dfrac{x+4+x+2x-4}{x\left(x+4\right)}=\dfrac{4x}{x\left(x+4\right)}=\dfrac{4}{x+4}=A\)
KH
5 tháng 7 2021
\(A=\dfrac{2}{x-1}\sqrt{\dfrac{\left(x-1\right)^2}{4x^2}}=\dfrac{2}{x-1}\left|\dfrac{x-1}{2x}\right|=\dfrac{\left|x-1\right|}{\left(x-1\right)\left|x\right|}\)
\(B=\left(x^2-4\right)\sqrt{\dfrac{9}{x^2-4x+4}}=\dfrac{3\left(x^2-4\right)}{\left|x-2\right|}\)
5 tháng 7 2021
a) Ta có: \(A=\dfrac{2}{x-1}\cdot\sqrt{\dfrac{x^2-2x+1}{4x^2}}\)
\(=\dfrac{2}{x-1}\cdot\dfrac{x-1}{2x}\)
\(=\dfrac{1}{x}\)
b) Ta có: \(\left(x^2-4\right)\cdot\sqrt{\dfrac{9}{x^2-4x+4}}\)
\(=\dfrac{\left(x-2\right)\left(x+2\right)\cdot3}{\left(x-2\right)^2}\)
\(=\dfrac{3x+6}{x-2}\)
23 tháng 12 2021
\(A=\left(\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x+1}{x\left(x+2\right)}-\dfrac{4}{x\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{x^2+x-2+x^2-x+2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x^2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x\left(x^2-2\right)\left(x-3\right)}{2x\left(x-2\right)\cdot\left(x+2\right)^2}=\dfrac{\left(x^2-2\right)\left(x-3\right)}{\left(x-2\right)\left(x+2\right)^2}\)
