Réitigh (2/x+5+4/x+3)div(3x+13/x^2+3x+15)

$$( \frac { 2 } { x + 5 } + \frac { 4 } { x + 3 } ) \div ( \frac { 3 x + 13 } { x ^ { 2 } + 3 x + 15 } )$$

Luacháil

$$\frac{2\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)}$$

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+5 agus x+3 ná \left(x+3\right)\left(x+5\right). Méadaigh \frac{2}{x+5} faoi \frac{x+3}{x+3}. Méadaigh \frac{4}{x+3} faoi \frac{x+5}{x+5}.

$$\frac{\frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}+\frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Tá an t-ainmneoir céanna ag \frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)} agus \frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\frac{2\left(x+3\right)+4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Déan iolrúcháin in 2\left(x+3\right)+4\left(x+5\right).

$$\frac{\frac{2x+6+4x+20}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Cumaisc téarmaí comhchosúla in: 2x+6+4x+20.

$$\frac{\frac{6x+26}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Roinn \frac{6x+26}{\left(x+3\right)\left(x+5\right)} faoi \frac{3x+13}{x^{2}+3x+15} trí \frac{6x+26}{\left(x+3\right)\left(x+5\right)} a mhéadú faoi dheilín \frac{3x+13}{x^{2}+3x+15}.

$$\frac{\left(6x+26\right)\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

$$\frac{2\left(3x+13\right)\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Cealaigh 3x+13 mar uimhreoir agus ainmneoir.

$$\frac{2\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)}$$

Fairsingigh an slonn.

$$\frac{2x^{2}+6x+30}{x^{2}+8x+15}$$

Fairsingigh

$$\frac{2\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)}$$

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+5 agus x+3 ná \left(x+3\right)\left(x+5\right). Méadaigh \frac{2}{x+5} faoi \frac{x+3}{x+3}. Méadaigh \frac{4}{x+3} faoi \frac{x+5}{x+5}.

$$\frac{\frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}+\frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Tá an t-ainmneoir céanna ag \frac{2\left(x+3\right)}{\left(x+3\right)\left(x+5\right)} agus \frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{\frac{2\left(x+3\right)+4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Déan iolrúcháin in 2\left(x+3\right)+4\left(x+5\right).

$$\frac{\frac{2x+6+4x+20}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Cumaisc téarmaí comhchosúla in: 2x+6+4x+20.

$$\frac{\frac{6x+26}{\left(x+3\right)\left(x+5\right)}}{\frac{3x+13}{x^{2}+3x+15}}$$

Roinn \frac{6x+26}{\left(x+3\right)\left(x+5\right)} faoi \frac{3x+13}{x^{2}+3x+15} trí \frac{6x+26}{\left(x+3\right)\left(x+5\right)} a mhéadú faoi dheilín \frac{3x+13}{x^{2}+3x+15}.

$$\frac{\left(6x+26\right)\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

$$\frac{2\left(3x+13\right)\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)\left(3x+13\right)}$$

Cealaigh 3x+13 mar uimhreoir agus ainmneoir.

$$\frac{2\left(x^{2}+3x+15\right)}{\left(x+3\right)\left(x+5\right)}$$

Fairsingigh an slonn.

$$\frac{2x^{2}+6x+30}{x^{2}+8x+15}$$