Atrisiniet 1/x^2-1-2/x^2+3x-4+1/x^2-2x-3

$$\frac { 1 } { x ^ { 2 } - 1 } - \frac { 2 } { x ^ { 2 } + 3 x - 4 } + \frac { 1 } { x ^ { 2 } - 2 x - 3 }$$

Izrēķināt

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

Īsās risinājuma darbības

Sadaliet reizinātājos x^{2}-1. Sadaliet reizinātājos x^{2}+3x-4.

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

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-1\right)\left(x+1\right) un \left(x-1\right)\left(x+4\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-1\right)\left(x+1\right)\left(x+4\right). Reiziniet \frac{1}{\left(x-1\right)\left(x+1\right)} reiz \frac{x+4}{x+4}. Reiziniet \frac{2}{\left(x-1\right)\left(x+4\right)} reiz \frac{x+1}{x+1}.

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

Tā kā \frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} un \frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

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

Veiciet reizināšanas darbības izteiksmē x+4-2\left(x+1\right).

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

Apvienojiet līdzīgos locekļus izteiksmē x+4-2x-2.

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

Sadaliet reizinātājos x^{2}-2x-3.

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

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-1\right)\left(x+1\right)\left(x+4\right) un \left(x-3\right)\left(x+1\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right). Reiziniet \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} reiz \frac{x-3}{x-3}. Reiziniet \frac{1}{\left(x-3\right)\left(x+1\right)} reiz \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)}.

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

Tā kā \frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} un \frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} ir viens un tas pats saucējs, saskaitiet tos, saskaitot to skaitītājus.

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

Veiciet reizināšanas darbības izteiksmē \left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right).

$$\frac{-x^{2}+3x+2x-6+x^{2}+4x-x-4}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē -x^{2}+3x+2x-6+x^{2}+4x-x-4.

$$\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

Paplašiniet \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right).

$$\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}$$

Diferencēt pēc x

$$\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}$$