Lutasin ang frac{R_{1}}{2R_{1}-R}-frac{R_{1}}{2R_{1}+R}

$$\frac { R _ { 1 } } { 2 R _ { 1 } - R } - \frac { R _ { 1 } } { 2 R _ { 1 } + R }$$

I-evaluate

$$\frac{2RR_{1}}{4R_{1}^{2}-R^{2}}$$

Maiikling Hakbang sa Solution

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 2R_{1}-R at 2R_{1}+R ay \left(R+2R_{1}\right)\left(-R+2R_{1}\right). I-multiply ang \frac{R_{1}}{2R_{1}-R} times \frac{R+2R_{1}}{R+2R_{1}}. I-multiply ang \frac{R_{1}}{2R_{1}+R} times \frac{-R+2R_{1}}{-R+2R_{1}}.

$$\frac{R_{1}\left(R+2R_{1}\right)}{\left(R+2R_{1}\right)\left(-R+2R_{1}\right)}-\frac{R_{1}\left(-R+2R_{1}\right)}{\left(R+2R_{1}\right)\left(-R+2R_{1}\right)}$$

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

$$\frac{R_{1}\left(R+2R_{1}\right)-R_{1}\left(-R+2R_{1}\right)}{\left(R+2R_{1}\right)\left(-R+2R_{1}\right)}$$

Gawin ang mga pag-multiply sa R_{1}\left(R+2R_{1}\right)-R_{1}\left(-R+2R_{1}\right).

$$\frac{R_{1}R+2R_{1}^{2}+R_{1}R-2R_{1}^{2}}{\left(R+2R_{1}\right)\left(-R+2R_{1}\right)}$$

Pagsamahin ang magkakatulad na term sa R_{1}R+2R_{1}^{2}+R_{1}R-2R_{1}^{2}.

$$\frac{2R_{1}R}{\left(R+2R_{1}\right)\left(-R+2R_{1}\right)}$$

Palawakin ang \left(R+2R_{1}\right)\left(-R+2R_{1}\right).

$$\frac{2R_{1}R}{-R^{2}+4R_{1}^{2}}$$

I-factor

$$\frac{2RR_{1}}{4R_{1}^{2}-R^{2}}$$