Datrys 3/1+x-2x^2+x/x-1

$$\frac { 3 } { 1 + x - 2 x ^ { 2 } } + \frac { x } { x - 1 }$$

Enrhifo

$$\frac{2x+3}{2x+1}$$

Camau Ateb Byr

Ffactora 1+x-2x^{2}.

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

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin \left(-x+1\right)\left(2x+1\right) a x-1 yw \left(x-1\right)\left(2x+1\right). Lluoswch \frac{3}{\left(-x+1\right)\left(2x+1\right)} â \frac{-1}{-1}. Lluoswch \frac{x}{x-1} â \frac{2x+1}{2x+1}.

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

Gan fod gan \frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} a \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

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

Gwnewch y gwaith lluosi yn 3\left(-1\right)+x\left(2x+1\right).

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

Dylech ffactoreiddio'r mynegiadau sydd heb eu ffactoreiddio eisoes yn \frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}.

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

Canslo x-1 yn y rhifiadur a'r enwadur.

$$\frac{2x+3}{2x+1}$$

Gwahaniaethu w.r.t. x

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

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

Ffactora 1+x-2x^{2}.

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

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin \left(-x+1\right)\left(2x+1\right) a x-1 yw \left(x-1\right)\left(2x+1\right). Lluoswch \frac{3}{\left(-x+1\right)\left(2x+1\right)} â \frac{-1}{-1}. Lluoswch \frac{x}{x-1} â \frac{2x+1}{2x+1}.

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

Gan fod gan \frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} a \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

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

Gwnewch y gwaith lluosi yn 3\left(-1\right)+x\left(2x+1\right).

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

Dylech ffactoreiddio'r mynegiadau sydd heb eu ffactoreiddio eisoes yn \frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}.

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

Canslo x-1 yn y rhifiadur a'r enwadur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+3}{2x+1})$$

Ar gyfer unrhyw ddau ffwythiant y mae modd eu gwahaniaethu, deilliad cyniferydd dau ffwythiant yw’r enwadur wedi’i luosi â deilliad yr enwadur wedi’i dynnu o’r rhifiadur wedi’i luosi â deilliad yr enwadur, y cwbl wedi’i rannu â’r enwadur wedi'i sgwario.

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

Deilliad polynomaial yw swm deilliadau ei dermau. Deilliad term cyson yw 0. Y deilliad o ax^{n} yw nax^{n-1}.

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

Gwneud y symiau.

$$\frac{\left(2x^{1}+1\right)\times 2x^{0}-\left(2x^{1}+3\right)\times 2x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

$$\frac{2x^{1}\times 2x^{0}+2x^{0}-\left(2x^{1}\times 2x^{0}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

I luosi pwerau sy’n rhannu’r un sail, ychwanegwch eu hesbonyddion.

$$\frac{2\times 2x^{1}+2x^{0}-\left(2\times 2x^{1}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

Gwneud y symiau.

$$\frac{4x^{1}+2x^{0}-\left(4x^{1}+6x^{0}\right)}{\left(2x^{1}+1\right)^{2}}$$

Tynnu’r cromfachau diangen.

$$\frac{4x^{1}+2x^{0}-4x^{1}-6x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(4-4\right)x^{1}+\left(2-6\right)x^{0}}{\left(2x^{1}+1\right)^{2}}$$

Tynnwch 4 o 4 a 6 o 2.

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

Ar gyfer unrhyw derm t, t^{1}=t.

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

Ar gyfer unrhyw derm t ac eithrio 0, t^{0}=1.

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