Question

Tính:

a) x² - 4/8x . x +190/x-2 + x² - 4/8x.x-194/x-2

b) 1/(x-5)(x-4) + 1/(x-4)(x-3) + 1/(x-3)(x-2) - 1/x-5

Answer 1

a) \(\frac{x^2-4}{8x}.\frac{x+190}{x-2}+\frac{x^2-4}{8x}.\frac{x-194}{x-2}\)

\(=\frac{x^2-4}{8x}\left(\frac{x+190}{x-2}+\frac{x-194}{x+2}\right)\)

\(=\frac{x^2-4}{8x}.\frac{2x-4}{x-2}\)

\(=\frac{x^2-4}{8x}.\frac{2\left(x-2\right)}{x-2}=\frac{x^2-4}{4x}\)

b) \(\frac{1}{\left(x-5\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-2\right)}-\frac{1}{x-5}\)

\(=\frac{1}{x-5}-\frac{1}{x-4}+\frac{1}{x-4}-\frac{1}{x-3}+\frac{1}{x-3}-\frac{1}{x-2}-\frac{1}{x-5}\)

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