Lutasin ang 2n^2-2n-12/12-6n-6n^2/frac{n^2-6n+9{3n^2+6n-9}}

$$\frac { \frac { 2 n ^ { 2 } - 2 n - 12 } { 12 - 6 n - 6 n ^ { 2 } } } { \frac { n ^ { 2 } - 6 n + 9 } { 3 n ^ { 2 } + 6 n - 9 } }$$

I-evaluate

$$-\frac{n+3}{n-3}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{2n^{2}-2n-12}{12-6n-6n^{2}} gamit ang \frac{n^{2}-6n+9}{3n^{2}+6n-9} sa pamamagitan ng pagmu-multiply sa \frac{2n^{2}-2n-12}{12-6n-6n^{2}} gamit ang reciprocal ng \frac{n^{2}-6n+9}{3n^{2}+6n-9}.

$$\frac{\left(2n^{2}-2n-12\right)\left(3n^{2}+6n-9\right)}{\left(12-6n-6n^{2}\right)\left(n^{2}-6n+9\right)}$$

I-factor ang mga expression na hindi pa na-factor.

$$\frac{2\times 3\left(n-3\right)\left(n-1\right)\left(n+2\right)\left(n+3\right)}{6\left(n+2\right)\left(-n+1\right)\left(n-3\right)^{2}}$$

I-extract ang negatibong sign sa -1+n.

$$\frac{-2\times 3\left(n-3\right)\left(n+2\right)\left(n+3\right)\left(-n+1\right)}{6\left(n+2\right)\left(-n+1\right)\left(n-3\right)^{2}}$$

I-cancel out ang 2\times 3\left(n-3\right)\left(n+2\right)\left(-n+1\right) sa parehong numerator at denominator.

$$\frac{-\left(n+3\right)}{n-3}$$

Palawakin ang expression.

$$\frac{-n-3}{n-3}$$

Palawakin

$$-\frac{n+3}{n-3}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{2n^{2}-2n-12}{12-6n-6n^{2}} gamit ang \frac{n^{2}-6n+9}{3n^{2}+6n-9} sa pamamagitan ng pagmu-multiply sa \frac{2n^{2}-2n-12}{12-6n-6n^{2}} gamit ang reciprocal ng \frac{n^{2}-6n+9}{3n^{2}+6n-9}.

$$\frac{\left(2n^{2}-2n-12\right)\left(3n^{2}+6n-9\right)}{\left(12-6n-6n^{2}\right)\left(n^{2}-6n+9\right)}$$

I-factor ang mga expression na hindi pa na-factor.

$$\frac{2\times 3\left(n-3\right)\left(n-1\right)\left(n+2\right)\left(n+3\right)}{6\left(n+2\right)\left(-n+1\right)\left(n-3\right)^{2}}$$

I-extract ang negatibong sign sa -1+n.

$$\frac{-2\times 3\left(n-3\right)\left(n+2\right)\left(n+3\right)\left(-n+1\right)}{6\left(n+2\right)\left(-n+1\right)\left(n-3\right)^{2}}$$

I-cancel out ang 2\times 3\left(n-3\right)\left(n+2\right)\left(-n+1\right) sa parehong numerator at denominator.

$$\frac{-\left(n+3\right)}{n-3}$$

Palawakin ang expression.

$$\frac{-n-3}{n-3}$$