Issolvi 1/3+1/2n+1-1/2n+3

$$\frac { 1 } { 3 } + \frac { 1 } { 2 n + 1 } - \frac { 1 } { 2 n + 3 }$$

Evalwa

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3 u 2n+1 huwa 3\left(2n+1\right). Immultiplika \frac{1}{3} b'\frac{2n+1}{2n+1}. Immultiplika \frac{1}{2n+1} b'\frac{3}{3}.

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

Billi \frac{2n+1}{3\left(2n+1\right)} u \frac{3}{3\left(2n+1\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

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

Ikkombina termini simili f'2n+1+3.

$$\frac{2n+4}{3\left(2n+1\right)}-\frac{1}{2n+3}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3\left(2n+1\right) u 2n+3 huwa 3\left(2n+1\right)\left(2n+3\right). Immultiplika \frac{2n+4}{3\left(2n+1\right)} b'\frac{2n+3}{2n+3}. Immultiplika \frac{1}{2n+3} b'\frac{3\left(2n+1\right)}{3\left(2n+1\right)}.

$$\frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)}-\frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)}$$

Billi \frac{\left(2n+4\right)\left(2n+3\right)}{3\left(2n+1\right)\left(2n+3\right)} u \frac{3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{\left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right)}{3\left(2n+1\right)\left(2n+3\right)}$$

Agħmel il-multiplikazzjonijiet fi \left(2n+4\right)\left(2n+3\right)-3\left(2n+1\right).

$$\frac{4n^{2}+6n+8n+12-6n-3}{3\left(2n+1\right)\left(2n+3\right)}$$

Ikkombina termini simili f'4n^{2}+6n+8n+12-6n-3.

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$

Espandi 3\left(2n+1\right)\left(2n+3\right).

$$\frac{4n^{2}+8n+9}{12n^{2}+24n+9}$$

Fattur

$$\frac{4n^{2}+8n+9}{3\left(2n+1\right)\left(2n+3\right)}$$