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\(P=\left(\dfrac{1}{ax-2}+\dfrac{1}{ax+2}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^2x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{ax+2+ax-2}{a^2x^2-4}+\dfrac{2ax}{a^2x^2+4}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{2ax\left(a^2x^2+4\right)+2ax\left(a^2x^2-4\right)}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\left(\dfrac{4a^3x^3}{a^4x^4-16}+\dfrac{4a^3x^3}{a^4x^4}\right)\cdot\dfrac{a^4x^4+16}{a^4x^4}\)
\(=\dfrac{8a^7x^7-64a^3x^3}{a^4x^4\left(a^4x^4-16\right)}\cdot\dfrac{a^4x^4+16}{a^4x^4}=\dfrac{\left(8a^7x^7-64a^3x^3\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}\)
\(=\dfrac{8a^3x^3\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^8x^8\left(a^4x^4-16\right)}=\dfrac{8\left(a^4x^4-8\right)\left(a^4x^4+16\right)}{a^5x^5\left(a^4x^4-16\right)}\)
\(a,A=\dfrac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}=\dfrac{4}{x+4}\\ b,B=\dfrac{x+4+x+2x-4}{x\left(x+4\right)}=\dfrac{4x}{x\left(x+4\right)}=\dfrac{4}{x+4}=A\)
\(A=\left(\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x+1}{x\left(x+2\right)}-\dfrac{4}{x\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{x^2+x-2+x^2-x+2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x^2-4}{x\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x-3\right)}{2\left(x+2\right)}\)
\(=\dfrac{2x\left(x^2-2\right)\left(x-3\right)}{2x\left(x-2\right)\cdot\left(x+2\right)^2}=\dfrac{\left(x^2-2\right)\left(x-3\right)}{\left(x-2\right)\left(x+2\right)^2}\)
a: |x-1|=3
=>x-1=3 hoặc x-1=-3
=>x=-2(nhận) hoặc x=4(loại)
Khi x=-2 thì \(A=\dfrac{4+4}{-2-4}=\dfrac{8}{-6}=\dfrac{-4}{3}\)
b: ĐKXĐ: x<>4; x<>-4
\(B=\dfrac{-\left(x+4\right)}{x-4}+\dfrac{x-4}{x+4}-\dfrac{4x^2}{\left(x-4\right)\left(x+4\right)}\)
\(=\dfrac{-x^2-8x-16+x^2-8x+16-4x^2}{\left(x-4\right)\left(x+4\right)}=\dfrac{-4x^2-16x}{\left(x-4\right)\left(x+4\right)}\)
=-4x/x-4
c: A+B
=-4x/x-4+x^2+4/x-4
=(x-2)^2/(x-4)
A+B>0
=>x-4>0
=>x>4