$\fraction{4}{x - 2} - \fraction{5}{x + 1}$

## 共享

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

\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} 和 \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} 的分母相同，因此將分子相減即可相減這兩個值。
\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)}

\frac{-x+14}{\left(x-2\right)\left(x+1\right)}

\frac{-x+14}{x^{2}-x-2}

\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})

\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})
\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} 和 \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} 的分母相同，因此將分子相減即可相減這兩個值。
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)})

\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{\left(x-2\right)\left(x+1\right)})

\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{x^{2}+x-2x-2})

\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+14}{x^{2}-x-2})

\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+14)-\left(-x^{1}+14\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}

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

\frac{\left(x^{2}-x^{1}-2\right)\left(-1\right)x^{0}-\left(-x^{1}+14\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}

\frac{x^{2}\left(-1\right)x^{0}-x^{1}\left(-1\right)x^{0}-2\left(-1\right)x^{0}-\left(-x^{1}+14\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
x^{2}-x^{1}-2 乘上 -x^{0}。
\frac{x^{2}\left(-1\right)x^{0}-x^{1}\left(-1\right)x^{0}-2\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-1\right)x^{0}+14\times 2x^{1}+14\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}
-x^{1}+14 乘上 2x^{1}-x^{0}。
\frac{-x^{2}-\left(-x^{1}\right)-2\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-x^{1}\right)+14\times 2x^{1}+14\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}

\frac{-x^{2}+x^{1}+2x^{0}-\left(-2x^{2}+x^{1}+28x^{1}-14x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}

\frac{x^{2}-28x^{1}+16x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}

\frac{x^{2}-28x+16x^{0}}{\left(x^{2}-x-2\right)^{2}}

\frac{x^{2}-28x+16\times 1}{\left(x^{2}-x-2\right)^{2}}

\frac{x^{2}-28x+16}{\left(x^{2}-x-2\right)^{2}}