Lutasin ang x-3/x^2-1divx^2-2x-3/x^2+2x+1+1/x-1

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

I-evaluate

$$\frac{2}{x-1}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{x-3}{x^{2}-1} gamit ang \frac{x^{2}-2x-3}{x^{2}+2x+1} sa pamamagitan ng pagmu-multiply sa \frac{x-3}{x^{2}-1} gamit ang reciprocal ng \frac{x^{2}-2x-3}{x^{2}+2x+1}.

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

I-factor ang mga expression na hindi pa na-factor sa \frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-2x-3\right)}.

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

I-cancel out ang \left(x-3\right)\left(x+1\right)^{2} sa parehong numerator at denominator.

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

Pagsamahin ang \frac{1}{x-1} at \frac{1}{x-1} para makuha ang 2\times \frac{1}{x-1}.

$$2\times \frac{1}{x-1}$$

Ipakita ang 2\times \frac{1}{x-1} bilang isang single fraction.

$$\frac{2}{x-1}$$

Palawakin

$$\frac{2}{x-1}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{x-3}{x^{2}-1} gamit ang \frac{x^{2}-2x-3}{x^{2}+2x+1} sa pamamagitan ng pagmu-multiply sa \frac{x-3}{x^{2}-1} gamit ang reciprocal ng \frac{x^{2}-2x-3}{x^{2}+2x+1}.

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

I-factor ang mga expression na hindi pa na-factor sa \frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-2x-3\right)}.

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

I-cancel out ang \left(x-3\right)\left(x+1\right)^{2} sa parehong numerator at denominator.

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

Pagsamahin ang \frac{1}{x-1} at \frac{1}{x-1} para makuha ang 2\times \frac{1}{x-1}.

$$2\times \frac{1}{x-1}$$

Ipakita ang 2\times \frac{1}{x-1} bilang isang single fraction.

$$\frac{2}{x-1}$$