Atrisiniet x/2x^2-7x+3+x-3/4x^2+4x-3-x^2+1/2x^2-3x

$$\frac { x } { 2 x ^ { 2 } - 7 x + 3 } + \frac { x - 3 } { 4 x ^ { 2 } + 4 x - 3 } - \frac { x ^ { 2 } + 1 } { 2 x ^ { 2 } - 3 x }$$

Izrēķināt

$$\frac{-4x^{5}+14x^{4}-4x^{3}+26x^{2}-12x-9}{x\left(x-3\right)\left(2x-1\right)\left(4x^{2}-9\right)}$$

Īsās risinājuma darbības

Sadaliet reizinātājos 2x^{2}-7x+3. Sadaliet reizinātājos 4x^{2}+4x-3.

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

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

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

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

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

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

$$\frac{2x^{2}+3x+x^{2}-3x-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{2x^{2}-3x}$$

Apvienojiet līdzīgos locekļus izteiksmē 2x^{2}+3x+x^{2}-3x-3x+9.

$$\frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{2x^{2}-3x}$$

Sadaliet reizinātājos 2x^{2}-3x.

$$\frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{x\left(2x-3\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-3\right)\left(2x-1\right)\left(2x+3\right) un x\left(2x-3\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right). Reiziniet \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} reiz \frac{x\left(2x-3\right)}{x\left(2x-3\right)}. Reiziniet \frac{x^{2}+1}{x\left(2x-3\right)} reiz \frac{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}.

$$\frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Tā kā \frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} un \frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right).

$$\frac{6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē 6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9.

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Paplašiniet x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right).

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{8x^{5}-28x^{4}-6x^{3}+63x^{2}-27x}$$

Paplašināt

$$\frac{-4x^{5}+14x^{4}-4x^{3}+26x^{2}-12x-9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)\left(2x^{2}-3x\right)}$$

Īsās risinājuma darbības

Sadaliet reizinātājos 2x^{2}-7x+3. Sadaliet reizinātājos 4x^{2}+4x-3.

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

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

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

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

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

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

$$\frac{2x^{2}+3x+x^{2}-3x-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{2x^{2}-3x}$$

Apvienojiet līdzīgos locekļus izteiksmē 2x^{2}+3x+x^{2}-3x-3x+9.

$$\frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{2x^{2}-3x}$$

Sadaliet reizinātājos 2x^{2}-3x.

$$\frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{x^{2}+1}{x\left(2x-3\right)}$$

Lai saskaitītu vai atņemtu izteiksmes, izvērsiet tās, vienādojot saucējus. \left(x-3\right)\left(2x-1\right)\left(2x+3\right) un x\left(2x-3\right) mazākais kopējais skaitlis, ar kuru dalāms bez atlikuma, ir x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right). Reiziniet \frac{3x^{2}-3x+9}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)} reiz \frac{x\left(2x-3\right)}{x\left(2x-3\right)}. Reiziniet \frac{x^{2}+1}{x\left(2x-3\right)} reiz \frac{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}.

$$\frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}-\frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Tā kā \frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} un \frac{\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)} ir viens un tas pats saucējs, atņemiet tos, atņemot to skaitītājus.

$$\frac{\left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right)}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Veiciet reizināšanas darbības izteiksmē \left(3x^{2}-3x+9\right)x\left(2x-3\right)-\left(x^{2}+1\right)\left(x-3\right)\left(2x-1\right)\left(2x+3\right).

$$\frac{6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Apvienojiet līdzīgos locekļus izteiksmē 6x^{4}-9x^{3}-6x^{3}+9x^{2}+18x^{2}-27x-4x^{5}+8x^{4}+15x^{3}-9x^{2}-4x^{3}+8x^{2}+15x-9.

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right)}$$

Paplašiniet x\left(x-3\right)\left(2x-3\right)\left(2x-1\right)\left(2x+3\right).

$$\frac{14x^{4}-4x^{3}+26x^{2}-12x-4x^{5}-9}{8x^{5}-28x^{4}-6x^{3}+63x^{2}-27x}$$