The image contains handwritten notes and a diagram, likely from a mathematics or physics context, but the text is too blurry to be deciphered accurately.

Kutokana na ubora wa picha, bado ni vigumu kusoma swali kwa uhakika. Hata hivyo, kwa kuzingatia muundo wa swali la awali na vigezo vinavyoonekana, nitaendelea na dhana kwamba swali ni kurahisisha usemi ufuatao:

Rahisisha $\frac{18x^2 - 2y^2}{3x - y}$.

Step 1: Toa kigezo cha kawaida kutoka kwa nambari (numerator). $\frac{18x^2 - 2y^2}{3x - y} = \frac{2(9x^2 - y^2)}{3x - y}$

Step 2: Tambua tofauti ya miraba katika nambari. Usemi $9x^2 - y^2$ unaweza kuandikwa kama $(3x)^2 - y^2$. $9x^2 - y^2 = (3x)^2 - y^2$

Step 3: Tumia mfumo wa tofauti ya miraba, $a^2 - b^2 = (a-b)(a+b)$, ambapo $a = 3x$ na $b = y$. $\frac{2((3x)^2 - y^2)}{3x - y} = \frac{2(3x - y)(3x + y)}{3x - y}$

Step 4: Futa vigezo vya kawaida $(3x - y)$ katika nambari na denominata (denominator). $\frac{2\cancel{(3x - y)}(3x + y)}{\cancel{3x - y}} = 2(3x + y)$

Jibu la mwisho ni: $\text{*2(3x + y)*}$ That's 2 down. 3 left today — send the next one.