Datrys 2n^2-n-1/2(n+1)-2(n-1)^2-(n-1)-1/2n

$$\frac { 2 n ^ { 2 } - n - 1 } { 2 ( n + 1 ) } - \frac { 2 ( n - 1 ) ^ { 2 } - ( n - 1 ) - 1 } { 2 n }$$

Enrhifo

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

Camau Ateb Byr

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

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

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

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

Gwnewch y gwaith lluosi yn \left(2n^{2}-n-1\right)n-\left(2\left(n-1\right)^{2}-\left(n-1\right)-1\right)\left(n+1\right).

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

Cyfuno termau tebyg yn 2n^{3}-n^{2}-n-2n^{3}+2n^{2}+2n-2+n^{2}-1+n+1.

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

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

$$\frac{2\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{2n\left(n+1\right)}$$

Canslo 2 yn y rhifiadur a'r enwadur.

$$\frac{\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n\left(n+1\right)}$$

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

$$\frac{\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n^{2}+n}$$

I ddod o hyd i wrthwyneb -\frac{1}{2}\sqrt{5}-\frac{1}{2}, dewch o hyd i wrthwyneb pob term.

$$\frac{\left(n+\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n^{2}+n}$$

I ddod o hyd i wrthwyneb \frac{1}{2}\sqrt{5}-\frac{1}{2}, dewch o hyd i wrthwyneb pob term.

$$\frac{\left(n+\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\left(n-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)}{n^{2}+n}$$

Defnyddio’r briodwedd ddosbarthu i luosi n+\frac{1}{2}\sqrt{5}+\frac{1}{2} â n-\frac{1}{2}\sqrt{5}+\frac{1}{2} a chyfuno termau tebyg.

$$\frac{n^{2}+n-\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{4}}{n^{2}+n}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{n^{2}+n-\frac{1}{4}\times 5+\frac{1}{4}}{n^{2}+n}$$

Lluosi -\frac{1}{4} a 5 i gael -\frac{5}{4}.

$$\frac{n^{2}+n-\frac{5}{4}+\frac{1}{4}}{n^{2}+n}$$

Adio -\frac{5}{4} a \frac{1}{4} i gael -1.

$$\frac{n^{2}+n-1}{n^{2}+n}$$

Ehangu

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

Camau Ateb Byr

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

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

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

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

Gwnewch y gwaith lluosi yn \left(2n^{2}-n-1\right)n-\left(2\left(n-1\right)^{2}-\left(n-1\right)-1\right)\left(n+1\right).

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

Cyfuno termau tebyg yn 2n^{3}-n^{2}-n-2n^{3}+2n^{2}+2n-2+n^{2}-1+n+1.

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

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

$$\frac{2\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{2n\left(n+1\right)}$$

Canslo 2 yn y rhifiadur a'r enwadur.

$$\frac{\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n\left(n+1\right)}$$

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

$$\frac{\left(n-\left(-\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n^{2}+n}$$

I ddod o hyd i wrthwyneb -\frac{1}{2}\sqrt{5}-\frac{1}{2}, dewch o hyd i wrthwyneb pob term.

$$\frac{\left(n+\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\left(n-\left(\frac{1}{2}\sqrt{5}-\frac{1}{2}\right)\right)}{n^{2}+n}$$

I ddod o hyd i wrthwyneb \frac{1}{2}\sqrt{5}-\frac{1}{2}, dewch o hyd i wrthwyneb pob term.

$$\frac{\left(n+\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)\left(n-\frac{1}{2}\sqrt{5}+\frac{1}{2}\right)}{n^{2}+n}$$

Defnyddio’r briodwedd ddosbarthu i luosi n+\frac{1}{2}\sqrt{5}+\frac{1}{2} â n-\frac{1}{2}\sqrt{5}+\frac{1}{2} a chyfuno termau tebyg.

$$\frac{n^{2}+n-\frac{1}{4}\left(\sqrt{5}\right)^{2}+\frac{1}{4}}{n^{2}+n}$$

Sgwâr \sqrt{5} yw 5.

$$\frac{n^{2}+n-\frac{1}{4}\times 5+\frac{1}{4}}{n^{2}+n}$$

Lluosi -\frac{1}{4} a 5 i gael -\frac{5}{4}.

$$\frac{n^{2}+n-\frac{5}{4}+\frac{1}{4}}{n^{2}+n}$$

Adio -\frac{5}{4} a \frac{1}{4} i gael -1.

$$\frac{n^{2}+n-1}{n^{2}+n}$$