Đề bài yêu cầu gì?

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

\(\frac{4}{x-5}-\frac{1}{x+5}+\frac{13x-x^2}{25-x^2}=\frac{4}{x-5}-\frac{1}{x+5}+\frac{x^2-13x}{x^2-25}\)

\(=\frac{4\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}-\frac{x-5}{\left(x-5\right)\left(x+5\right)}+\frac{x^2-13x}{\left(x-5\right)\left(x+5\right)}\)

\(=\frac{4x+20-x+5+x^2-13x}{\left(x-5\right)\left(x+5\right)}\)

\(=\frac{x^2-10x+25}{\left(x-5\right)\left(x+5\right)}=\frac{\left(x-5\right)^2}{\left(x-5\right)\left(x+5\right)}=\frac{x-5}{x+5}\)

a: \(A=\dfrac{2}{\sqrt{x}+3}-\dfrac{2}{\sqrt{x}-3}\)

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

\(=\dfrac{-12}{x-9}\)

a)\(\frac{3y}{4x}+\frac{5y}{4x}=\frac{3y+5y}{4x}=\frac{8y}{4x}=\frac{2y}{x}\)

b)\(\frac{x^2+1}{2x-4}-\frac{7x}{2-x}=\frac{x^2+1}{2\left(x-2\right)}-\frac{-7x}{x-2}\)

\(=\frac{x^2+1}{2\left(x-2\right)}-\frac{-7x\times2}{\left(x-2\right)\times2}=\frac{x^2+1+14x}{2\left(x-2\right)}\)

a, \(\frac{x+1}{2x+6}+\frac{2x+3}{x^2+3x}=\frac{x+1}{2\left(x+3\right)}+\frac{3x+2}{x\left(x+3\right)}\)

\(=\frac{x^2+x}{2x\left(x+3\right)}+\frac{6x+4}{2x\left(x+3\right)}=\frac{x^2+7x+4}{2x\left(x+3\right)}\)

b, Sua de :  \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\)

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

\(\frac{1}{2.x}-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{45.46}=-2\)

\(\frac{1}{2.x}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{45.46}\right)=-2\)

\(\frac{1}{2.x}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{45}-\frac{1}{46}\right)=-2\)

\(\frac{1}{2.x}-\left(1-\frac{1}{46}\right)\)

\(\frac{1}{2.x}-\frac{45}{46}=-2\)

\(\frac{1}{2.x}=-2+\frac{45}{46}\)

\(\frac{1}{2.x}=\frac{-47}{46}\)

\(2x=\frac{46}{-47}\)

\(x=\frac{46}{-47}:2=\frac{-23}{47}\)