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\(\frac{x^2+2}{2xy^3}-\frac{2x+2}{2xy^3}=\frac{x^2+2-2x-2}{2xy^3}=\frac{x^2-2x}{2xy^3}=\frac{x\left(x-2\right)}{2xy^3}=\frac{x-2}{2y^3}\)
\(\frac{4}{x-5}-\frac{1}{x+5}+\frac{13x-x^2}{25-x^2}=\frac{4}{x-5}-\frac{1}{x+5}+\frac{x^2-13x}{x^2-25}\)
\(=\frac{4\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}-\frac{x-5}{\left(x-5\right)\left(x+5\right)}+\frac{x^2-13x}{\left(x-5\right)\left(x+5\right)}\)
\(=\frac{4x+20-x+5+x^2-13x}{\left(x-5\right)\left(x+5\right)}\)
\(=\frac{x^2-10x+25}{\left(x-5\right)\left(x+5\right)}=\frac{\left(x-5\right)^2}{\left(x-5\right)\left(x+5\right)}=\frac{x-5}{x+5}\)
\(\frac{1}{x-2}-\frac{1}{x+2}+\frac{4x-x^2}{4-x^2}\)
\(=\frac{x+2}{\left(x-2\right)\left(x+2\right)}-\frac{x-2}{\left(x+2\right)\left(x-2\right)}+\frac{4x-x^2}{\left(2-x\right)\left(x+2\right)}\)
\(=\frac{x+2-x+2-4x+x^2}{\left(x+2\right)\left(x-2\right)}=\frac{-4x+4+x^2}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}=\frac{x-2}{x+2}\)
\(\frac{1}{x-2}-\frac{1}{x+2}+\frac{4x-x^2}{4-x^2}\)
\(=\frac{1}{x-2}-\frac{1}{x+2}+\frac{x^2-4x}{x^2-4}\)
\(=\frac{1}{x-2}-\frac{1}{x+2}+\frac{x^2-4x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+2}{\left(x-2\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+2\right)}+\frac{x^2-4x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x+2-x+2+x^2-4x}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}=\frac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\frac{x-2}{x+2}\)
a, \(B=\left(\frac{2x+1}{2x-1}+\frac{4}{1-4x^2}-\frac{2x-1}{2x+1}\right):\frac{x^2+2}{2x+1}\)
\(=\left(\frac{2x+1}{2x-1}+\frac{4}{\left(1-2x\right)\left(2x+1\right)}-\frac{2x-1}{2x+1}\right):\frac{x^2+2}{2x+1}\)
\(=\left(\frac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\frac{4}{\left(2x-1\right)\left(2x+1\right)}-\frac{\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}\right):\frac{x^2+2}{2x+1}\)
\(=\left(\frac{4x^2+4x+1-4-4x^2+4x-1}{\left(2x-1\right)\left(2x+1\right)}\right):\frac{x^2+2}{2x+1}\)
\(=\frac{8x-4}{\left(2x-1\right)\left(2x+1\right)}.\frac{2x+1}{x^2+2}=\frac{8x-4}{\left(2x-1\right)\left(x^2+2\right)}\)
b, Thay x = -1 ta được : \(\frac{9\left(-1\right)-4}{\left[2\left(-1\right)-1\right]\left[\left(-1\right)^2+2\right]}=-\frac{13}{-9}=\frac{13}{9}\)
A = (x - 1)(x + 3) - (x - 2)(5x - 4)
A = x2 + 2x - 3 - 5x2 + 14x - 8
A = -4x2 + 16x - 11
B = (3a - 2b)(9a2 + 6ab - 4b2)
B = 27a3 + 18a2b - 12ab2 - 18a2b - 12ab2 + 8b3
B = 27a3 -24ab2 + 8b3
C = (x - 1)(x + 1) - (2x - 3)(4 - 5x)
C = x2 - 1 - 8x + 10x + 12 - 15x
C = x2 - 13x + 11
a)\(\frac{x^2+xy}{x^2-y^2}=\frac{x\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\frac{x}{x-y}\)
b) \(\frac{4}{x+2}+\frac{3}{x-2}+\frac{-5x-2}{x^2-4}\)
\(=\frac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{-5x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{4x-8+3x+6-5x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{2x-4}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{2}{x+2}\)