Réitigh 3/2x-5-4/x-3

$$\frac{ 3 }{ 2x-5 } - \frac{ 4 }{ x-3 }$$

Luacháil

$$\frac{11-5x}{\left(x-3\right)\left(2x-5\right)}$$

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

$$\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)}-\frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}$$

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

$$\frac{3\left(x-3\right)-4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}$$

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

$$\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)}$$

Cumaisc téarmaí comhchosúla in: 3x-9-8x+20.

$$\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)}$$

Fairsingigh \left(x-3\right)\left(2x-5\right)

$$\frac{-5x+11}{2x^{2}-11x+15}$$

Difreálaigh w.r.t. x

$$\frac{2\left(\left(5x-11\right)^{2}-6\right)}{5\left(\left(x-3\right)\left(2x-5\right)\right)^{2}}$$

Céimeanna ag Baint Úsáid as Riail na nDíorthach don Líon

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 2x-5 agus x-3 ná \left(x-3\right)\left(2x-5\right). Méadaigh \frac{3}{2x-5} faoi \frac{x-3}{x-3}. Méadaigh \frac{4}{x-3} faoi \frac{2x-5}{2x-5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)}-\frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-3\right)-4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)})$$

Cumaisc téarmaí comhchosúla in: 3x-9-8x+20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)})$$

Cuir an t-airí dáileacháin i bhfeidhm trí gach téarma de x-3 a iolrú faoi gach téarma de 2x-5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-5x-6x+15})$$

Comhcheangail -5x agus -6x chun -11x a fháil.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-11x+15})$$

Do dhá fheidhm indifreáilte ar bith, is ionann díorthach líon an dá fheidhme agus an t-ainmneoir méadaithe faoi dhíorthach an uimhreora lúide an t-uimhreoir méadaithe faoi dhíorthach an ainmneora, agus iad ar fad roinnte faoin ainmneoir cearnaithe.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}+11)-\left(-5x^{1}+11\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-11x^{1}+15)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{1-1}-\left(-5x^{1}+11\right)\left(2\times 2x^{2-1}-11x^{1-1}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Simpligh.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Méadaigh 2x^{2}-11x^{1}+15 faoi -5x^{0}.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Méadaigh -5x^{1}+11 faoi 4x^{1}-11x^{0}.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}\times 4x^{1}-5x^{1}\left(-11\right)x^{0}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Chun cumhachtaí an bhoinn chéanna a mhéadú, suimigh a n-easpónaint.

$$\frac{2\left(-5\right)x^{2}-11\left(-5\right)x^{1}+15\left(-5\right)x^{0}-\left(-5\times 4x^{1+1}-5\left(-11\right)x^{1}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Simpligh.

$$\frac{-10x^{2}+55x^{1}-75x^{0}-\left(-20x^{2}+55x^{1}+44x^{1}-121x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Cuir téarmaí cosúla le chéile.

$$\frac{10x^{2}-44x^{1}+46x^{0}}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Do théarma ar bith t, t^{1}=t.

$$\frac{10x^{2}-44x+46x^{0}}{\left(2x^{2}-11x+15\right)^{2}}$$

Do théarma ar bith t ach amháin 0, t^{0}=1.

$$\frac{10x^{2}-44x+46\times 1}{\left(2x^{2}-11x+15\right)^{2}}$$

Do théarma ar bith t, t\times 1=t agus 1t=t.

$$\frac{10x^{2}-44x+46}{\left(2x^{2}-11x+15\right)^{2}}$$