Réitigh x^2+x/x^2-25+x^2-1/x^2+11x+30

$$\frac { x ^ { 2 } + x } { x ^ { 2 } - 25 } + \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 11 x + 30 }$$

Luacháil

$$\frac{\left(x+1\right)\left(2x^{2}+5\right)}{\left(x+6\right)\left(x^{2}-25\right)}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}-25. Fachtóirigh x^{2}+11x+30.

$$\frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)}+\frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-5\right)\left(x+5\right) agus \left(x+5\right)\left(x+6\right) ná \left(x-5\right)\left(x+5\right)\left(x+6\right). Méadaigh \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} faoi \frac{x+6}{x+6}. Méadaigh \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} faoi \frac{x-5}{x-5}.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Tá an t-ainmneoir céanna ag \frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} agus \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Déan iolrúcháin in \left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right).

$$\frac{x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Cumaisc téarmaí comhchosúla in: x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5.

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Fairsingigh \left(x-5\right)\left(x+5\right)\left(x+6\right)

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$

Fairsingigh

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x+6\right)\left(x^{2}-25\right)}$$

Céimeanna gearra réitigh

Fachtóirigh x^{2}-25. Fachtóirigh x^{2}+11x+30.

$$\frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)}+\frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de \left(x-5\right)\left(x+5\right) agus \left(x+5\right)\left(x+6\right) ná \left(x-5\right)\left(x+5\right)\left(x+6\right). Méadaigh \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} faoi \frac{x+6}{x+6}. Méadaigh \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} faoi \frac{x-5}{x-5}.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Tá an t-ainmneoir céanna ag \frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} agus \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Déan iolrúcháin in \left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right).

$$\frac{x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Cumaisc téarmaí comhchosúla in: x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5.

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

Fairsingigh \left(x-5\right)\left(x+5\right)\left(x+6\right)

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$