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

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

Evalwa

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

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} b'\frac{6x+10y}{5x-25y} billi timmultiplika \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} bir-reċiproku ta' \frac{6x+10y}{5x-25y}.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}.

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

Annulla \left(3x-5y\right)\left(3x+5y\right) fin-numeratur u d-denominatur.

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

Immultiplika \frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)} b'\frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla 9x^{2}+15xy+25y^{2} fin-numeratur u d-denominatur.

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

Uża l-propjetà distributtiva biex timmultiplika 5 b'x-5y.

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'9x^{2}-18xy+5y^{2}.

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

Espandi

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

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} b'\frac{6x+10y}{5x-25y} billi timmultiplika \frac{9x^{2}-25y^{2}}{27x^{3}-125y^{3}} bir-reċiproku ta' \frac{6x+10y}{5x-25y}.

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

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{\left(9x^{2}-25y^{2}\right)\left(5x-25y\right)}{\left(27x^{3}-125y^{3}\right)\left(6x+10y\right)}.

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

Annulla \left(3x-5y\right)\left(3x+5y\right) fin-numeratur u d-denominatur.

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

Immultiplika \frac{5\left(x-5y\right)}{2\left(9x^{2}+15xy+25y^{2}\right)} b'\frac{9x^{2}+15xy+25y^{2}}{9x^{2}-18xy+5y^{2}} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Annulla 9x^{2}+15xy+25y^{2} fin-numeratur u d-denominatur.

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

Uża l-propjetà distributtiva biex timmultiplika 5 b'x-5y.

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

Uża l-propjetà distributtiva biex timmultiplika 2 b'9x^{2}-18xy+5y^{2}.

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