Datrys f(x)=2/x-3/x+1

$$f ( x ) = \frac { 2 } { x } - \frac { 3 } { x + 1 }$$

Enrhifo

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

Camau Ateb Byr

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

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

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

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

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

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

Cyfuno termau tebyg yn 2x+2-3x.

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

Ehangu x\left(x+1\right).

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

Gwahaniaethu w.r.t. x

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

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

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

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

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

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

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

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

Cyfuno termau tebyg yn 2x+2-3x.

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

Defnyddio’r briodwedd ddosbarthu i luosi x â x+1.

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

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.

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

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

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

Symleiddio.

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

Lluoswch x^{2}+x^{1} â -x^{0}.

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

Lluoswch -x^{1}+2 â 2x^{1}+x^{0}.

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

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

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

Symleiddio.

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

Cyfuno termau sydd yr un peth.

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

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

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

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

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