Lutasin ang 3x+2/x^2+3x-10-5x+11/x^2+4x-5+4x-1/x^2-3x+2

$$\frac{ 3x+2 }{ { x }^{ 2 } +3x-10 } - \frac{ 5x+11 }{ { x }^{ 2 } +4x-5 } + \frac{ 4x-1 }{ { x }^{ 2 } -3x+2 }$$

I-evaluate

$$\frac{\left(x+1\right)\left(2x+15\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}$$

Maiikling Hakbang sa Solution

I-factor out ang x^{2}+3x-10. I-factor out ang x^{2}+4x-5.

$$\frac{3x+2}{\left(x-2\right)\left(x+5\right)}-\frac{5x+11}{\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. Ang least common multiple ng \left(x-2\right)\left(x+5\right) at \left(x-1\right)\left(x+5\right) ay \left(x-2\right)\left(x-1\right)\left(x+5\right). I-multiply ang \frac{3x+2}{\left(x-2\right)\left(x+5\right)} times \frac{x-1}{x-1}. I-multiply ang \frac{5x+11}{\left(x-1\right)\left(x+5\right)} times \frac{x-2}{x-2}.

$$\frac{\left(3x+2\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}-\frac{\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Dahil may parehong denominator ang \frac{\left(3x+2\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)} at \frac{\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{\left(3x+2\right)\left(x-1\right)-\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Gawin ang mga pag-multiply sa \left(3x+2\right)\left(x-1\right)-\left(5x+11\right)\left(x-2\right).

$$\frac{3x^{2}-3x+2x-2-5x^{2}+10x-11x+22}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Pagsamahin ang magkakatulad na term sa 3x^{2}-3x+2x-2-5x^{2}+10x-11x+22.

$$\frac{-2x^{2}-2x+20}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

I-factor out ang x^{2}-3x+2.

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

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. Ang least common multiple ng \left(x-2\right)\left(x-1\right)\left(x+5\right) at \left(x-2\right)\left(x-1\right) ay \left(x-2\right)\left(x-1\right)\left(x+5\right). I-multiply ang \frac{4x-1}{\left(x-2\right)\left(x-1\right)} times \frac{x+5}{x+5}.

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

Dahil may parehong denominator ang \frac{-2x^{2}-2x+20}{\left(x-2\right)\left(x-1\right)\left(x+5\right)} at \frac{\left(4x-1\right)\left(x+5\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}, pagsamahin ang mga ito sa pamamagitan ng pagsasama sa mga numerator ng mga ito.

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

Gawin ang mga pag-multiply sa -2x^{2}-2x+20+\left(4x-1\right)\left(x+5\right).

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

Pagsamahin ang magkakatulad na term sa -2x^{2}-2x+20+4x^{2}+20x-x-5.

$$\frac{2x^{2}+17x+15}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}$$

Palawakin ang \left(x-2\right)\left(x-1\right)\left(x+5\right).

$$\frac{2x^{2}+17x+15}{x^{3}+2x^{2}-13x+10}$$

Palawakin

$$\frac{2x^{2}+17x+15}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}$$

Maiikling Hakbang sa Solution

I-factor out ang x^{2}+3x-10. I-factor out ang x^{2}+4x-5.

$$\frac{3x+2}{\left(x-2\right)\left(x+5\right)}-\frac{5x+11}{\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. Ang least common multiple ng \left(x-2\right)\left(x+5\right) at \left(x-1\right)\left(x+5\right) ay \left(x-2\right)\left(x-1\right)\left(x+5\right). I-multiply ang \frac{3x+2}{\left(x-2\right)\left(x+5\right)} times \frac{x-1}{x-1}. I-multiply ang \frac{5x+11}{\left(x-1\right)\left(x+5\right)} times \frac{x-2}{x-2}.

$$\frac{\left(3x+2\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}-\frac{\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Dahil may parehong denominator ang \frac{\left(3x+2\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)} at \frac{\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{\left(3x+2\right)\left(x-1\right)-\left(5x+11\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Gawin ang mga pag-multiply sa \left(3x+2\right)\left(x-1\right)-\left(5x+11\right)\left(x-2\right).

$$\frac{3x^{2}-3x+2x-2-5x^{2}+10x-11x+22}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

Pagsamahin ang magkakatulad na term sa 3x^{2}-3x+2x-2-5x^{2}+10x-11x+22.

$$\frac{-2x^{2}-2x+20}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}+\frac{4x-1}{x^{2}-3x+2}$$

I-factor out ang x^{2}-3x+2.

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

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. Ang least common multiple ng \left(x-2\right)\left(x-1\right)\left(x+5\right) at \left(x-2\right)\left(x-1\right) ay \left(x-2\right)\left(x-1\right)\left(x+5\right). I-multiply ang \frac{4x-1}{\left(x-2\right)\left(x-1\right)} times \frac{x+5}{x+5}.

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

Dahil may parehong denominator ang \frac{-2x^{2}-2x+20}{\left(x-2\right)\left(x-1\right)\left(x+5\right)} at \frac{\left(4x-1\right)\left(x+5\right)}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}, pagsamahin ang mga ito sa pamamagitan ng pagsasama sa mga numerator ng mga ito.

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

Gawin ang mga pag-multiply sa -2x^{2}-2x+20+\left(4x-1\right)\left(x+5\right).

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

Pagsamahin ang magkakatulad na term sa -2x^{2}-2x+20+4x^{2}+20x-x-5.

$$\frac{2x^{2}+17x+15}{\left(x-2\right)\left(x-1\right)\left(x+5\right)}$$

Palawakin ang \left(x-2\right)\left(x-1\right)\left(x+5\right).

$$\frac{2x^{2}+17x+15}{x^{3}+2x^{2}-13x+10}$$