Question:লঘিষ্ট আকারে প্রকাশ কর: ক. `(4x^2y^3z^5)/(9x^5y^2z^5)` খ. `(16(2x)^4(3y)^5)/((3x)^3.(2y)^6)` গ. `(x^3y + xy^3)/(x^2y^3 + x^3y^2)` ঘ. `((a - b) (a + b))/(a^3 - b^3)` ঙ. `(x^2 - 6x + 5)/(x^2 - 25)` চ. `(x^2 - 7x + 12)/(x^2 - 9x + 20)` ছ. `((x^3 - y^3) (x^2 - xy + y^2))/((x^2 - y^2) (x^3 + y^3))` জ. `(a^2 - b^2 - 2bc - c^2)/(a^2 + 2ab + b^2 - c^2)`
Answer ক. `(4x^2y^3z^5)/(9x^5y^2z^3)` 4 ও 9 এর গ.সা,গু = 1 `x^2` ও `x^5` '' '' = `x^2` `y^3` ও `y^2` '' '' =` y^2` `z^5` ও `z^3` '' '' =` z^3` `:. 4x^2y^3z^5` ও `9x^5y^2z^3` এর গ.সা.গু দ্বারা ভাগ করে পাই, `= x^2y^2z^3` `(4x^2y^3z^5)/(9x^5y^2z^3)` এর লব ও হরকে `x^2y^2z^3` দ্বারা ভাগ করে পাই, `(4xyz^2)/(9x^3)` :. নির্ণেয় লঘিষ্ট রুপ `= (4yz)^2/(9x^3)` উত্তর `: (4yz)^2/(9x^3)` খ. `(16(2x)^4(3y)^5)/((3x)^3.(2y)^6)` `= (16. 16x^4. 243y^5)/(27x^3. 64y^6)` `= (62208x^4y^5)/(1728x^3y^6)` 62208 ও 1728 এর গ.সা,গু = 1728 `x^4` ও `x^3` '' '' =` x^3` `y^5` ও `y^6` '' '' = `y^5` `:. x^4y^5` ও `1728x^3y^6` এর গ.সা.গু `= 1728x^3y^5` `(62208 x^4y^5)/(1728x^3y^6)` এর লব হরকে `1728x^3y^5` দ্বার ভাগ করে পাই, `(36x)/y` :. নির্ণেয় লঘিষ্ট রুপ `= (36x)/y` উত্তর`: (36x)/y` গ. `(x^3y + xy^3)/(x^2y^3 + x^3y^2)` `= (xy(x^2 + y^2))/(x^2y^2(y + x))` `= (x^2 + y^2)/(xy(x + y)` :. নির্ণেয় লঘিষ্ট রুপ `= (x^2 + y^2)/(xy(x + y)` উত্তর `: (x^2 + y^2)/(xy(x + y)` ঘ. `((a - b)(a + b))/(a^3 - b^3)` `= ((a - b)(a + b))/((a - b)(a^2 + ab + b^2))` `= (a + b)/(a^2 + ab + b^2)` :. নির্ণেয় লঘিষ্ট রুপ `= (a + b)/(a^2 + ab + b^2)` `: (a + b)/(a^2 + ab + b^2)` ঙ. `(x^2 - 6x + 5)/(x^2 - 25)` `= (x^2 - 5x - x + 5)/(x^2 - 5^2)` `= (x(x - 5) - 1(x - 5))/((x + 5)(x - 5))` `= (x - 1)/(x + 5)` :. নির্ণেয় লঘিষ্ট রুপ `= (x - 1)/(x + 5)` উত্তর: `= (x - 1)/(x + 5)` চ. `(x^2 - 7x + 12)/(x^2 - 9x + 20)` `= (x^2 - 4x - 3x + 12)/(x^2 - 5x - 4x + 20)` `= (x(x - 4) - 3(x - 4))/(x(x - 5) - 4(x - 5))` `= ((x - 4)(x - 3))/((x - 5) (x - 4))` `= (x - 3)/(x - 5)` :. নির্ণেয় লঘিষ্ট রুপ `= (x - 3)/(x - 5)` উত্তর `= (x - 3)/(x - 5)` ছ. `((x^3 - y^3)(x^2 - xy + y^2))/((x^2 - y^2)(x^3 + y^3))` `= ((x - y)(x^2 + xy + y^2)(x^2 - xy + y^2))/((x + y)(x - y)(x + y) (x^2 - xy + y^2))` `= (x^2 + xy + y^2)/(x + y)^2` নির্ণেয় লঘিষ্ট রুপ `= (x^2 + xy + y^2)/(x + y)^2` উত্তর `: (x^2 + xy + y^2)/(x + y)^2` জ. `(a^2 - b^2 - 2bc - c^2)/(a^2 + 2ab + b^2 - c^2)` `= (a^2 - (b^2 + 2bc + c^2))/((a^2 + 2ab + b^2) - c^2)` `= (a^2 - (b + c))^2/((a + b)^2 - c^2)` `= ((a + b + c)(a - b - c))/((a + b + c)(a + b - c))` `= (a - b - c)/(a + b - c)` :. নির্ণেয় লঘিষ্ট রুপ `= (a - b - c)/(a + b - c)` উত্তর `= (a - b - c)/(a + b - c)`
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lghisht akare prokasho karo: ka. `(4x^2y^3z^5)/(9x^5y^2z^5)` kh. `(16(2x)^4(3y)^5)/((3x)^3.(2y)^6)` ga. `(x^3y + xy^3)/(x^2y^3 + x^3y^2)` gh. `((a - b) (a + b))/(a^3 - b^3)` ঙ. `(x^2 - 6x + 5)/(x^2 - 25)` ch. `(x^2 - 7x + 12)/(x^2 - 9x + 20)` cho. `((x^3 - y^3) (x^2 - xy + y^2))/((x^2 - y^2) (x^3 + y^3))` ja. `(a^2 - b^2 - 2bc - c^2)/(a^2 + 2ab + b^2 - c^2)`