Lahenda x^2-6x+5/x^2-x-20divx-1/x+4divx^2-4x-5/x^2-10x+25

$$\frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } - x - 20 } \div \frac { x - 1 } { x + 4 } \div \frac { x ^ { 2 } - 4 x - 5 } { x ^ { 2 } - 10 x + 25 }$$

Arvuta

$$\frac{x-5}{x+1}$$

Lühike lahenduskäik

Jagage \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} väärtusega \frac{x^{2}-4x-5}{x^{2}-10x+25}, korrutades \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} väärtuse \frac{x^{2}-4x-5}{x^{2}-10x+25} pöördväärtusega.

$$\frac{\frac{x^{2}-6x+5}{x^{2}-x-20}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Kui avaldised pole tehtes \frac{x^{2}-6x+5}{x^{2}-x-20} veel teguriteks lahutatud, tehke seda.

$$\frac{\frac{\left(x-5\right)\left(x-1\right)}{\left(x-5\right)\left(x+4\right)}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Taandage x-5 nii lugejas kui ka nimetajas.

$$\frac{\frac{x-1}{x+4}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Avaldage \frac{x-1}{x+4}\left(x^{2}-10x+25\right) ühe murdarvuna.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Avaldage \frac{x-1}{x+4}\left(x^{2}-4x-5\right) ühe murdarvuna.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}}$$

Jagage \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} väärtusega \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}, korrutades \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} väärtuse \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4} pöördväärtusega.

$$\frac{\left(x-1\right)\left(x^{2}-10x+25\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)\left(x^{2}-4x-5\right)}$$

Taandage \left(x-1\right)\left(x+4\right) nii lugejas kui ka nimetajas.

$$\frac{x^{2}-10x+25}{x^{2}-4x-5}$$

Kui avaldised pole juba teguriteks lahutatud, tehke seda.

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

Taandage x-5 nii lugejas kui ka nimetajas.

$$\frac{x-5}{x+1}$$

Laienda

$$\frac{x-5}{x+1}$$

Lühike lahenduskäik

Jagage \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} väärtusega \frac{x^{2}-4x-5}{x^{2}-10x+25}, korrutades \frac{\frac{x^{2}-6x+5}{x^{2}-x-20}}{\frac{x-1}{x+4}} väärtuse \frac{x^{2}-4x-5}{x^{2}-10x+25} pöördväärtusega.

$$\frac{\frac{x^{2}-6x+5}{x^{2}-x-20}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Kui avaldised pole tehtes \frac{x^{2}-6x+5}{x^{2}-x-20} veel teguriteks lahutatud, tehke seda.

$$\frac{\frac{\left(x-5\right)\left(x-1\right)}{\left(x-5\right)\left(x+4\right)}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Taandage x-5 nii lugejas kui ka nimetajas.

$$\frac{\frac{x-1}{x+4}\left(x^{2}-10x+25\right)}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Avaldage \frac{x-1}{x+4}\left(x^{2}-10x+25\right) ühe murdarvuna.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{x-1}{x+4}\left(x^{2}-4x-5\right)}$$

Avaldage \frac{x-1}{x+4}\left(x^{2}-4x-5\right) ühe murdarvuna.

$$\frac{\frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4}}{\frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}}$$

Jagage \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} väärtusega \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4}, korrutades \frac{\left(x-1\right)\left(x^{2}-10x+25\right)}{x+4} väärtuse \frac{\left(x-1\right)\left(x^{2}-4x-5\right)}{x+4} pöördväärtusega.

$$\frac{\left(x-1\right)\left(x^{2}-10x+25\right)\left(x+4\right)}{\left(x+4\right)\left(x-1\right)\left(x^{2}-4x-5\right)}$$

Taandage \left(x-1\right)\left(x+4\right) nii lugejas kui ka nimetajas.

$$\frac{x^{2}-10x+25}{x^{2}-4x-5}$$

Kui avaldised pole juba teguriteks lahutatud, tehke seda.

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

Taandage x-5 nii lugejas kui ka nimetajas.

$$\frac{x-5}{x+1}$$