\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(=\frac{x\left(x+2\right)}{2\left(x+5\right)}+\frac{x-5}{x}+\frac{5\left(10-x\right)}{2x\left(x+5\right)}\)

\(=\frac{x^2\left(x+2\right)+2\left(x+5\right)\left(x-5\right)+5\left(10-x\right)}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3-3x+2x^2}{2x\left(x+5\right)}=\frac{x\left(x^2+2x-3\right)}{2x\left(x+5\right)}\)

\(=\frac{\left(x-1\right)\left(x+3\right)}{2\left(x+5\right)}\)

\(B=\frac{x+5}{2x}-\frac{x-6}{5-x}-\frac{2x^2-2x-50}{2x^2-10x}\)

\(B=\frac{x+5}{2x}-\left(\frac{x-6}{5-x}\right)-\left(\frac{2x^2-2x-50}{2x^2-10x}\right)\)

\(B=\frac{-2x^4+30x^3-150x^2+250x}{-4x^4+40x^3-100x^2}\)

\(B=\frac{-2x^3+30x^2-150x+250}{-4x^3+40x^2-100x}\)

\(B=\frac{-x^3+15x^2-75x+125}{-2x^3+20x^2-50x}\)

\(B=\frac{\left(-x+5\right)\left(x-5\right)\left(x-5\right)}{2x\left(-x+5\right)\left(x-5\right)}\)

\(B=\frac{x-5}{2x}\)

\(a,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\) (x khác -3; khác 0)

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

\(b,\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}\) (x khác 0 , khác 1/2 khác -1/2 )

\(=\left(\frac{\left(2x+1\right)^2}{\left(2x-1\right)\left(2x+1\right)}-\frac{\left(2x-1\right)^2}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)

\(=\left(\frac{4x^2+4x+1}{\left(2x-1\right)\left(2x+1\right)}-\frac{4x^2-4x+1}{\left(2x-1\right)\left(2x+1\right)}\right).\frac{10x-5}{4x}\)

\(=\frac{8x}{\left(2x-1\right)\left(2x+1\right)}.\frac{5.\left(2x-1\right)}{4x}=\frac{10}{2x+1}\)

\(c,\frac{x^2+x}{5x^2-10x+5}:\frac{3x+3}{5x-5}\) (x khác 1 ; khác -1)

\(=\frac{x.\left(x+1\right)}{5.\left(x^2-2x+1\right)}.\frac{5x-5}{3x+3}=\frac{x.\left(x+1\right)}{5.\left(x-1\right)^2}.\frac{5\left(x-1\right)}{3.\left(x+1\right)}=\frac{x}{3.\left(x-1\right)}=\frac{x}{3x-3}\)

a) ĐKXĐ: \(\begin{cases}x\ne0\\x\ne-5\end{cases}\)

b) A = \(\frac{5x-50-\left(x-5\right)\left(2x+10\right)-x\left(x^2+2x\right)}{2x^2+10x}\) = \(\frac{-x^3-4x^2+5x}{2x^2+10x}\) = \(\frac{-x^2-4x+5}{2x+10}\) 

= \(\frac{\left(1-x\right)\left(x+5\right)}{2\left(x+5\right)}\) =\(\frac{1-x}{2}\) 

c) Để A = 3 => \(\frac{1-x}{2}\) = 3 =>1 - x = 6 => x = - 7(t/m ĐKXĐ)

a) \(P=\frac{x}{2x-2}+\frac{x^2+1}{2-2x^2}\)

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

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

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

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

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

\(P=\frac{x-1}{2\left(x-1\right)\left(x+1\right)}=\frac{1}{2\left(x+1\right)}\)

b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x\left(x+2\right)}{2\left(x+5\right)}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^2\left(x+2\right)+2\left(x+5\right)\left(x-5\right)+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}=\frac{x^2+4x-5}{2\left(x+5\right)}\)

a) \(P=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)

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

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

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

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

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

b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{5x-5x}{2x\left(x+5\right)}\)

\(=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x-5\right)\left(x+5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3-x^2+5x^2-5x}{2x\left(x+5\right)}\)

\(=\frac{x^2\left(x-1\right)+5x\left(x-1\right)}{2x\left(x+5\right)}\)

\(=\frac{\left(x-1\right)\left(x^2+5x\right)}{2x\left(x+5\right)}\)

\(=\frac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}\)

\(=\frac{x-1}{2}\)

xin lỗi phần a làm sai mình làm lại