Lutasin ang 4w/w^2+9w+14-2w+5/w^2+3w-28

$$\frac { 4 w } { w ^ { 2 } + 9 w + 14 } - \frac { 2 w + 5 } { w ^ { 2 } + 3 w - 28 }$$

I-evaluate

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Maiikling Hakbang sa Solution

I-factor out ang w^{2}+9w+14. I-factor out ang w^{2}+3w-28.

$$\frac{4w}{\left(w+2\right)\left(w+7\right)}-\frac{2w+5}{\left(w-4\right)\left(w+7\right)}$$

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(w+2\right)\left(w+7\right) at \left(w-4\right)\left(w+7\right) ay \left(w-4\right)\left(w+2\right)\left(w+7\right). I-multiply ang \frac{4w}{\left(w+2\right)\left(w+7\right)} times \frac{w-4}{w-4}. I-multiply ang \frac{2w+5}{\left(w-4\right)\left(w+7\right)} times \frac{w+2}{w+2}.

$$\frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}-\frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Dahil may parehong denominator ang \frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} at \frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Gawin ang mga pag-multiply sa 4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right).

$$\frac{4w^{2}-16w-2w^{2}-4w-5w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Pagsamahin ang magkakatulad na term sa 4w^{2}-16w-2w^{2}-4w-5w-10.

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Palawakin ang \left(w-4\right)\left(w+2\right)\left(w+7\right).

$$\frac{2w^{2}-25w-10}{w^{3}+5w^{2}-22w-56}$$

Palawakin

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Maiikling Hakbang sa Solution

I-factor out ang w^{2}+9w+14. I-factor out ang w^{2}+3w-28.

$$\frac{4w}{\left(w+2\right)\left(w+7\right)}-\frac{2w+5}{\left(w-4\right)\left(w+7\right)}$$

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(w+2\right)\left(w+7\right) at \left(w-4\right)\left(w+7\right) ay \left(w-4\right)\left(w+2\right)\left(w+7\right). I-multiply ang \frac{4w}{\left(w+2\right)\left(w+7\right)} times \frac{w-4}{w-4}. I-multiply ang \frac{2w+5}{\left(w-4\right)\left(w+7\right)} times \frac{w+2}{w+2}.

$$\frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}-\frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Dahil may parehong denominator ang \frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} at \frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Gawin ang mga pag-multiply sa 4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right).

$$\frac{4w^{2}-16w-2w^{2}-4w-5w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Pagsamahin ang magkakatulad na term sa 4w^{2}-16w-2w^{2}-4w-5w-10.

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Palawakin ang \left(w-4\right)\left(w+2\right)\left(w+7\right).

$$\frac{2w^{2}-25w-10}{w^{3}+5w^{2}-22w-56}$$