Réitigh [1.5-(x^{4}-frac{x^{4}+1}{x^{2}+1})*frac{(x^{2}+1)(x-4)}{x^7+6x^6-x-6}]:x^2+29x+78/3x^2+12x-36=

$$[ 1.5 - ( x ^ { 4 } - \frac { x ^ { 4 } + 1 } { x ^ { 2 } + 1 } ) \cdot \frac { ( x ^ { 2 } + 1 ) ( x - 4 ) } { x ^ { 7 } + 6 x ^ { 6 } - x - 6 } ] : \frac { x ^ { 2 } + 29 x + 78 } { 3 x ^ { 2 } + 12 x - 36 } =$$

Luacháil

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

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh x^{4} faoi \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1.5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Tá an t-ainmneoir céanna ag \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} agus \frac{x^{4}+1}{x^{2}+1} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{1.5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Déan iolrúcháin in x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1.5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cumaisc téarmaí comhchosúla in: x^{6}+x^{4}-x^{4}-1.

$$\frac{1.5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Méadaigh \frac{x^{6}-1}{x^{2}+1} faoi \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$\frac{1.5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cealaigh x^{2}+1 mar uimhreoir agus ainmneoir.

$$\frac{1.5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1.5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cealaigh \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) mar uimhreoir agus ainmneoir.

$$\frac{1.5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Roinn 1.5-\frac{x-4}{x+6} faoi \frac{x^{2}+29x+78}{3x^{2}+12x-36} trí 1.5-\frac{x-4}{x+6} a mhéadú faoi dheilín \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1.5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Úsáid an t-airí dáileach chun 1.5-\frac{x-4}{x+6} a mhéadú faoi 3x^{2}+12x-36.

$$\frac{4.5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh -3\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh \frac{-3\left(x-4\right)}{x+6}x^{2} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh -12\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh \frac{-12\left(x-4\right)}{x+6}x mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh 36\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 18x-54 faoi \frac{x+6}{x+6}.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{\left(18x-54\right)\left(x+6\right)}{x+6} agus \frac{-3\left(x-4\right)x^{2}}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4.5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{30x^{2}+54x-324-3x^{3}}{x+6} agus \frac{-12\left(x-4\right)x}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{18x^{2}+102x-324-3x^{3}}{x+6} agus \frac{36\left(x-4\right)}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4.5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4.5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Cealaigh x+6 mar uimhreoir agus ainmneoir.

$$\frac{4.5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Fairsingigh an slonn.

$$\frac{4.5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Comhcheangail 4.5x^{2} agus -3x^{2} chun 1.5x^{2} a fháil.

$$\frac{1.5x^{2}+36x-78}{x^{2}+29x+78}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Cealaigh x+26 mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

$$\frac{\frac{3}{2}x-3}{x+3}$$

Fairsingigh

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

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh x^{4} faoi \frac{x^{2}+1}{x^{2}+1}.

$$\frac{1.5-\left(\frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1}-\frac{x^{4}+1}{x^{2}+1}\right)\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Tá an t-ainmneoir céanna ag \frac{x^{4}\left(x^{2}+1\right)}{x^{2}+1} agus \frac{x^{4}+1}{x^{2}+1} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{1.5-\frac{x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right)}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Déan iolrúcháin in x^{4}\left(x^{2}+1\right)-\left(x^{4}+1\right).

$$\frac{1.5-\frac{x^{6}+x^{4}-x^{4}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cumaisc téarmaí comhchosúla in: x^{6}+x^{4}-x^{4}-1.

$$\frac{1.5-\frac{x^{6}-1}{x^{2}+1}\times \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Méadaigh \frac{x^{6}-1}{x^{2}+1} faoi \frac{\left(x^{2}+1\right)\left(x-4\right)}{x^{7}+6x^{6}-x-6} tríd an uimhreoir a mhéadú faoin uimhreoir agus an t-ainmneoir a mhéadú faoin ainmneoir.

$$\frac{1.5-\frac{\left(x^{6}-1\right)\left(x^{2}+1\right)\left(x-4\right)}{\left(x^{2}+1\right)\left(x^{7}+6x^{6}-x-6\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cealaigh x^{2}+1 mar uimhreoir agus ainmneoir.

$$\frac{1.5-\frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{\left(x-4\right)\left(x^{6}-1\right)}{x^{7}+6x^{6}-x-6}.

$$\frac{1.5-\frac{\left(x-4\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+6\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Cealaigh \left(x-1\right)\left(x+1\right)\left(x^{2}+x+1\right)\left(x^{2}-x+1\right) mar uimhreoir agus ainmneoir.

$$\frac{1.5-\frac{x-4}{x+6}}{\frac{x^{2}+29x+78}{3x^{2}+12x-36}}$$

Roinn 1.5-\frac{x-4}{x+6} faoi \frac{x^{2}+29x+78}{3x^{2}+12x-36} trí 1.5-\frac{x-4}{x+6} a mhéadú faoi dheilín \frac{x^{2}+29x+78}{3x^{2}+12x-36}.

$$\frac{\left(1.5-\frac{x-4}{x+6}\right)\left(3x^{2}+12x-36\right)}{x^{2}+29x+78}$$

Úsáid an t-airí dáileach chun 1.5-\frac{x-4}{x+6} a mhéadú faoi 3x^{2}+12x-36.

$$\frac{4.5x^{2}+18x-54-3\times \frac{x-4}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh -3\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)}{x+6}x^{2}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh \frac{-3\left(x-4\right)}{x+6}x^{2} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}-12\times \frac{x-4}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh -12\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)}{x+6}x+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh \frac{-12\left(x-4\right)}{x+6}x mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+36\times \frac{x-4}{x+6}}{x^{2}+29x+78}$$

Scríobh 36\times \frac{x-4}{x+6} mar chodán aonair.

$$\frac{4.5x^{2}+18x-54+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Méadaigh 18x-54 faoi \frac{x+6}{x+6}.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)}{x+6}+\frac{-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{\left(18x-54\right)\left(x+6\right)}{x+6} agus \frac{-3\left(x-4\right)x^{2}}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{\left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in \left(18x-54\right)\left(x+6\right)-3\left(x-4\right)x^{2}.

$$\frac{4.5x^{2}+\frac{18x^{2}+108x-54x-324-3x^{3}+12x^{2}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 18x^{2}+108x-54x-324-3x^{3}+12x^{2}.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}}{x+6}+\frac{-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{30x^{2}+54x-324-3x^{3}}{x+6} agus \frac{-12\left(x-4\right)x}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in 30x^{2}+54x-324-3x^{3}-12\left(x-4\right)x.

$$\frac{4.5x^{2}+\frac{30x^{2}+54x-324-3x^{3}-12x^{2}+48x}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 30x^{2}+54x-324-3x^{3}-12x^{2}+48x.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}}{x+6}+\frac{36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Tá an t-ainmneoir céanna ag \frac{18x^{2}+102x-324-3x^{3}}{x+6} agus \frac{36\left(x-4\right)}{x+6} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36\left(x-4\right)}{x+6}}{x^{2}+29x+78}$$

Déan iolrúcháin in 18x^{2}+102x-324-3x^{3}+36\left(x-4\right).

$$\frac{4.5x^{2}+\frac{18x^{2}+102x-324-3x^{3}+36x-144}{x+6}}{x^{2}+29x+78}$$

Cumaisc téarmaí comhchosúla in: 18x^{2}+102x-324-3x^{3}+36x-144.

$$\frac{4.5x^{2}+\frac{18x^{2}+138x-468-3x^{3}}{x+6}}{x^{2}+29x+78}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{18x^{2}+138x-468-3x^{3}}{x+6}.

$$\frac{4.5x^{2}+\frac{3\left(x+6\right)\left(-x^{2}+12x-26\right)}{x+6}}{x^{2}+29x+78}$$

Cealaigh x+6 mar uimhreoir agus ainmneoir.

$$\frac{4.5x^{2}+3\left(-x^{2}+12x-26\right)}{x^{2}+29x+78}$$

Fairsingigh an slonn.

$$\frac{4.5x^{2}-3x^{2}+36x-78}{x^{2}+29x+78}$$

Comhcheangail 4.5x^{2} agus -3x^{2} chun 1.5x^{2} a fháil.

$$\frac{1.5x^{2}+36x-78}{x^{2}+29x+78}$$

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana.

$$\frac{3\left(\frac{1}{2}x-1\right)\left(x+26\right)}{\left(x+3\right)\left(x+26\right)}$$

Cealaigh x+26 mar uimhreoir agus ainmneoir.

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

Fairsingigh an slonn.

$$\frac{\frac{3}{2}x-3}{x+3}$$