Lutasin ang frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}}div6x+10y/5x-25y*9x^2+15xy+25y^2/9x^2-18xy+5y^2=

$$\frac { 9 x ^ { 2 } - 25 y ^ { 2 } } { 27 x ^ { 3 } - 125 y ^ { 3 } } \div \frac { 6 x + 10 y } { 5 x - 25 y } \cdot \frac { 9 x ^ { 2 } + 15 x y + 25 y ^ { 2 } } { 9 x ^ { 2 } - 18 x y + 5 y ^ { 2 } } =$$

I-evaluate

$$\frac{5\left(x-5y\right)}{2\left(3x-y\right)\left(3x-5y\right)}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} gamit ang \frac{6x+10y}{5x-25y} sa pamamagitan ng pagmu-multiply sa \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} gamit ang reciprocal ng \frac{6x+10y}{5x-25y}.

$$\frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-factor ang mga expression na hindi pa na-factor sa \frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}.

$$\frac{5\left(x-5y\right)\left(3x-5y\right)\left(3x+5y\right)}{2\left(3x-5y\right)\left(3x+5y\right)\left(9x^{2}+15xy+25y^{2}\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-cancel out ang \left(3x-5y\right)\left(3x+5y\right) sa parehong numerator at denominator.

$$\frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-multiply ang \frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)} sa \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}} sa pamamagitan ng pag-multiply ng numerator sa numerator at denominator sa denominator.

$$\frac{5\left(x-5y\right)\left(9x^{2}+15xy+25y^{2}\right)}{2\left(9x^{2}+15xy+25y^{2}\right)\left(9x^{2}-18xy+5y^{2}\right)}$$

I-cancel out ang 9x^{2}+15xy+25y^{2} sa parehong numerator at denominator.

$$\frac{5\left(x-5y\right)}{2\left(9x^{2}-18xy+5y^{2}\right)}$$

Gamitin ang distributive property para i-multiply ang 5 gamit ang x-5y.

$$\frac{5x-25y}{2\left(9x^{2}-18xy+5y^{2}\right)}$$

Gamitin ang distributive property para i-multiply ang 2 gamit ang 9x^{2}-18xy+5y^{2}.

$$\frac{5x-25y}{18x^{2}-36xy+10y^{2}}$$

Palawakin

$$-\frac{5\left(5y-x\right)}{2\left(y-3x\right)\left(5y-3x\right)}$$

Maiikling Hakbang sa Solution

I-divide ang \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} gamit ang \frac{6x+10y}{5x-25y} sa pamamagitan ng pagmu-multiply sa \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} gamit ang reciprocal ng \frac{6x+10y}{5x-25y}.

$$\frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-factor ang mga expression na hindi pa na-factor sa \frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}.

$$\frac{5\left(x-5y\right)\left(3x-5y\right)\left(3x+5y\right)}{2\left(3x-5y\right)\left(3x+5y\right)\left(9x^{2}+15xy+25y^{2}\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-cancel out ang \left(3x-5y\right)\left(3x+5y\right) sa parehong numerator at denominator.

$$\frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)}\times \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}}$$

I-multiply ang \frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)} sa \frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}} sa pamamagitan ng pag-multiply ng numerator sa numerator at denominator sa denominator.

$$\frac{5\left(x-5y\right)\left(9x^{2}+15xy+25y^{2}\right)}{2\left(9x^{2}+15xy+25y^{2}\right)\left(9x^{2}-18xy+5y^{2}\right)}$$

I-cancel out ang 9x^{2}+15xy+25y^{2} sa parehong numerator at denominator.

$$\frac{5\left(x-5y\right)}{2\left(9x^{2}-18xy+5y^{2}\right)}$$

Gamitin ang distributive property para i-multiply ang 5 gamit ang x-5y.

$$\frac{5x-25y}{2\left(9x^{2}-18xy+5y^{2}\right)}$$

Gamitin ang distributive property para i-multiply ang 2 gamit ang 9x^{2}-18xy+5y^{2}.

$$\frac{5x-25y}{18x^{2}-36xy+10y^{2}}$$