Issolvi frac{x^{2}-8x+15}{5x^2+10x}divx^2-9/10x^2*x^2+5x+6/2x-10

$$\frac { x ^ { 2 } - 8 x + 15 } { 5 x ^ { 2 } + 10 x } \div \frac { x ^ { 2 } - 9 } { 10 x ^ { 2 } } \times \frac { x ^ { 2 } + 5 x + 6 } { 2 x - 10 }$$

Evalwa

$$x$$

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{x^{2}-8x+15}{5x^{2}+10x} b'\frac{x^{2}-9}{10x^{2}} billi timmultiplika \frac{x^{2}-8x+15}{5x^{2}+10x} bir-reċiproku ta' \frac{x^{2}-9}{10x^{2}}.

$$\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}.

$$\frac{10\left(x-5\right)\left(x-3\right)x^{2}}{5x\left(x-3\right)\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

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

$$\frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

Immultiplika \frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)} b'\frac{x^{2}+5x+6}{2x-10} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{2x\left(x-5\right)\left(x^{2}+5x+6\right)}{\left(x+2\right)\left(x+3\right)\left(2x-10\right)}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati.

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

Annulla 2\left(x-5\right)\left(x+2\right)\left(x+3\right) fin-numeratur u d-denominatur.

$$x$$

Iddifferenzja w.r.t. x

$$1$$

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

Iddividi \frac{x^{2}-8x+15}{5x^{2}+10x} b'\frac{x^{2}-9}{10x^{2}} billi timmultiplika \frac{x^{2}-8x+15}{5x^{2}+10x} bir-reċiproku ta' \frac{x^{2}-9}{10x^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10\left(x-5\right)\left(x-3\right)x^{2}}{5x\left(x-3\right)\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

Immultiplika \frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)} b'\frac{x^{2}+5x+6}{2x-10} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)\left(x^{2}+5x+6\right)}{\left(x+2\right)\left(x+3\right)\left(2x-10\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)\left(x+2\right)\left(x+3\right)}{2\left(x-5\right)\left(x+2\right)\left(x+3\right)})$$

Annulla 2\left(x-5\right)\left(x+2\right)\left(x+3\right) fin-numeratur u d-denominatur.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

$$x^{1-1}$$

Naqqas 1 minn 1.

$$x^{0}$$

Għal kwalunkwe terminu t ħlief 0, t^{0}=1.

$$1$$