Lutasin ang g(x)=x^3+6x/x^2-36divx^2+3x-40/x^2+2x-48

$$g ( x ) = \frac { x ^ { 3 } + 6 x } { x ^ { 2 } - 36 } \div \frac { x ^ { 2 } + 3 x - 40 } { x ^ { 2 } + 2 x - 48 }$$

I-evaluate

$$\frac{x\left(x^{2}+6\right)}{\left(x-5\right)\left(x+6\right)}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{x^{3}+6x}{x^{2}-36} gamit ang \frac{x^{2}+3x-40}{x^{2}+2x-48} sa pamamagitan ng pagmu-multiply sa \frac{x^{3}+6x}{x^{2}-36} gamit ang reciprocal ng \frac{x^{2}+3x-40}{x^{2}+2x-48}.

$$\frac{\left(x^{3}+6x\right)\left(x^{2}+2x-48\right)}{\left(x^{2}-36\right)\left(x^{2}+3x-40\right)}$$

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

$$\frac{x\left(x-6\right)\left(x+8\right)\left(x^{2}+6\right)}{\left(x-6\right)\left(x-5\right)\left(x+6\right)\left(x+8\right)}$$

I-cancel out ang \left(x-6\right)\left(x+8\right) sa parehong numerator at denominator.

$$\frac{x\left(x^{2}+6\right)}{\left(x-5\right)\left(x+6\right)}$$

Palawakin ang expression.

$$\frac{x^{3}+6x}{x^{2}+x-30}$$

Palawakin

$$\frac{x^{3}+6x}{\left(x-5\right)\left(x+6\right)}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{x^{3}+6x}{x^{2}-36} gamit ang \frac{x^{2}+3x-40}{x^{2}+2x-48} sa pamamagitan ng pagmu-multiply sa \frac{x^{3}+6x}{x^{2}-36} gamit ang reciprocal ng \frac{x^{2}+3x-40}{x^{2}+2x-48}.

$$\frac{\left(x^{3}+6x\right)\left(x^{2}+2x-48\right)}{\left(x^{2}-36\right)\left(x^{2}+3x-40\right)}$$

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

$$\frac{x\left(x-6\right)\left(x+8\right)\left(x^{2}+6\right)}{\left(x-6\right)\left(x-5\right)\left(x+6\right)\left(x+8\right)}$$

I-cancel out ang \left(x-6\right)\left(x+8\right) sa parehong numerator at denominator.

$$\frac{x\left(x^{2}+6\right)}{\left(x-5\right)\left(x+6\right)}$$

Palawakin ang expression.

$$\frac{x^{3}+6x}{x^{2}+x-30}$$