Réitigh 8/x+3+12/x+7/frac{5x+23{x^2+10x+21}}

$$\frac { \frac { 8 } { x + 3 } + \frac { 12 } { x + 7 } } { \frac { 5 x + 23 } { x ^ { 2 } + 10 x + 21 } }$$

Luacháil

$$4$$

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de x+3 agus x+7 ná \left(x+3\right)\left(x+7\right). Méadaigh \frac{8}{x+3} faoi \frac{x+7}{x+7}. Méadaigh \frac{12}{x+7} faoi \frac{x+3}{x+3}.

$$\frac{\frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)}+\frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Tá an t-ainmneoir céanna ag \frac{8\left(x+7\right)}{\left(x+3\right)\left(x+7\right)} agus \frac{12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\frac{8\left(x+7\right)+12\left(x+3\right)}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Déan iolrúcháin in 8\left(x+7\right)+12\left(x+3\right).

$$\frac{\frac{8x+56+12x+36}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Cumaisc téarmaí comhchosúla in: 8x+56+12x+36.

$$\frac{\frac{20x+92}{\left(x+3\right)\left(x+7\right)}}{\frac{5x+23}{x^{2}+10x+21}}$$

Roinn \frac{20x+92}{\left(x+3\right)\left(x+7\right)} faoi \frac{5x+23}{x^{2}+10x+21} trí \frac{20x+92}{\left(x+3\right)\left(x+7\right)} a mhéadú faoi dheilín \frac{5x+23}{x^{2}+10x+21}.

$$\frac{\left(20x+92\right)\left(x^{2}+10x+21\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

$$\frac{4\left(x+3\right)\left(x+7\right)\left(5x+23\right)}{\left(x+3\right)\left(x+7\right)\left(5x+23\right)}$$

Cealaigh \left(x+3\right)\left(x+7\right)\left(5x+23\right) mar uimhreoir agus ainmneoir.

$$4$$

Fachtóirigh

$$2^{2}$$