Question

Tính (rút gọn):

\(\frac{2}{\left(x-3\right).\left(x-1\right)}+\frac{-7}{\left(x+4\right).\left(x-3\right)}+\frac{4}{x.\left(x+4\right)}\)

Answer 1

\(\frac{2}{\left(x-3\right).\left(x-1\right)}+\frac{-7}{\left(x+4\right).\left(x-3\right)}+\frac{4}{x.\left(x+4\right)}\)

\(=\frac{2x.\left(x+4\right)}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{-7x.\left(x-1\right)}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{4.\left(x-3\right).\left(x-1\right)}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

\(=\frac{2x^2+8x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{-7x^2+7x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{\left(4x-12\right).\left(x-1\right)}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

\(=\frac{2x^2+8x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{-7x^2+7x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{4x^2-4x-12x+12}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

\(=\frac{2x^2+8x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{-7x^2+7x}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}+\frac{4x^2-16x+12}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

\(=\frac{2x^2+8x-7x^2+7x+4x^2-16x+12}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

\(=\frac{-x^2-x+12}{x.\left(x-3\right).\left(x-1\right).\left(x+4\right)}\)

Chúc bạn học tốt!

Answer 2

\(\frac{2}{\left(x-3\right)\left(x-1\right)}+-\frac{7}{\left(x+4\right)\left(x-3\right)}+\frac{4}{x\left(x+4\right)}\)

\(=\frac{2x\left(x+4\right)}{x\left(x+4\right)\left(x-1\right)\left(x-3\right)}+\frac{-7x\left(x-1\right)}{x\left(x-1\right)\left(x+4\right)\left(x-3\right)}+\frac{4\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x-3\right)x\left(x+4\right)}\)

\(=\frac{2x^2+8x}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}+\frac{-7x^2+7x}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}+\frac{4\left(x^2-4x+3\right)}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}\)

\(=\frac{2x^2+8x+7x^2+7x+4\left(x^2-4x+3\right)}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}\)

\(=\frac{-x^2-x+12}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}\)

\(=\frac{-\left(x^2+4x-3x-12\right)}{x\left(x+4\right)\left(x-3\right)\left(x-1\right)}\)

\(=\frac{-\left(x+4\right)\left(x-3\right)}{x\left(x+4\right)\left(x-3\right)\left(x1\right)}\)

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