অনুশীলনী ৫.১

অষ্টম শ্রেণি (মাধ্যমিক)- গণিত - বীজগণিতীয় ভগ্নাংশ - অনুশীলনী ৫.১ | NCTB BOOK

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(১)
লঘিষ্ঠ আকারে প্রকাশ কর :

(ক)
$\frac{4 x^{2} y^{3} z^{5}}{9 x^{5} y^{2} z^{3}}$

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(খ)
$\frac{16 {(2 x)}^{4} {(3 y)}^{5}}{{(3 x)}^{3} . {(2 y)}^{6}}$

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(গ)
$\frac{x^{3} y + x y^{3}}{x^{2} y^{3} + x^{3} y^{2}}$

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(ঘ)
$\frac{(a - b) (a + b)}{a^{3} - b^{3}}$

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(ঙ)
$\frac{x^{2} - 6 x + 5}{x^{2} - 25}$

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(চ)
$\frac{x^{2} - 7 x + 12}{x^{2} - 9 x + 20}$

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(ছ)
$\frac{(x^{3} - y^{3}) (x^{2} - x y + y^{2})}{(x^{2} - y^{2}) (x^{3} + y^{3})}$

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(জ)
$\frac{a^{2} - b^{2} - 2 b c - c^{2}}{a^{2} + 2 a b + b^{2} - c^{2}}$

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(২)
সাধারণ হরবিশিষ্ট ভগ্নাংশে প্রকাশ কর :

(ক)
$\frac{x^{2}}{x y}, \frac{y^{2}}{y x}, \frac{z^{2}}{z x}$

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(খ)
$\frac{x - y}{x y}, \frac{y - z}{y z}, \frac{z - x}{z x}$

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(গ)
$\frac{x}{x - y}, \frac{y}{x + y}, \frac{z}{x (x + y)}$

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(ঘ)
$\frac{x + y}{{(x - y)}^{2}}, \frac{x - y}{x^{3} + y^{3}}, \frac{y - z}{x^{2} - y^{2}}$

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(ঙ)
$\frac{a}{a^{3} + b^{3}}, \frac{b}{(a^{2} + a b + b^{2})}, \frac{c}{a^{3} - b^{3}}$

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(চ)
$\frac{1}{x^{2} - 5 x + 6}, \frac{1}{x^{2} - 7 x + 12}, \frac{1}{x^{2} - 9 x + 20}$

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(ছ)
$\frac{a - b}{a^{2} b^{2}}, \frac{b - c}{b^{2} c^{2}}, \frac{c - a}{c^{2} a^{2}}$

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(জ)
$\frac{x - y}{x + y}, \frac{y - z}{y + z}, \frac{z - x}{z + x}$

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(৩)
যোগফল নির্ণয় কর :

(ক)
$\frac{a - b}{a} + \frac{a + b}{b}$

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(খ)
$\frac{a}{b c} + \frac{b}{c a} + \frac{c}{a b}$

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(গ)
$\frac{x - y}{x} + \frac{y - z}{y} + \frac{z - x}{z}$

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(ঘ)
$\frac{x + y}{x - y} + \frac{x - y}{x + y}$

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(ঙ)
$\frac{1}{x^{1} - 3 x + 2} + \frac{1}{x^{2} - 4 x + 3} + \frac{1}{x^{2} - 5 x + 4}$

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(চ)
$\frac{1}{a^{2} - b^{2}} + \frac{1}{a^{2} + a b + b^{2}} + \frac{1}{a^{2} - a b + b^{2}}$

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(ছ)
$\frac{1}{x - 2} + \frac{1}{x + 2} + \frac{4}{x^{2} - 4}$

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(জ)
$\frac{1}{x^{2} - 1} + \frac{1}{x^{4} - 1} + \frac{4}{x^{8} - 1}$

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(৪)
বিয়োগফল নির্ণয় কর :

(ক)
$\frac{a}{x - 3} - \frac{a^{2}}{x^{2} - 9}$

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(খ)
$\frac{1}{y (x - y)} - \frac{1}{x (x + y)}$

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(গ)
$\frac{x + 1}{1 + x + x^{2}} - \frac{x - y}{1 - x + x^{2}}$

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(ঘ)
$\frac{a^{2} + 16 b^{2}}{a^{2} - 16 b^{2}} - \frac{a - 4 b}{a + 4 b}$

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(ঙ)
$\frac{1}{x - y} - \frac{x^{2} - x y + y^{2}}{x^{3} + y^{3}}$

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(৫)
সরল কর :

(ক)
$\frac{x - y}{x y} + \frac{y - z}{y z} + \frac{z - x}{z x}$

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(খ)
$\frac{x - y}{(x + y) (y + z)} + \frac{y - z}{(y + z) (z + x)} + \frac{z - x}{(z + x) (x + y)}$

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(গ)
$\frac{y}{(x - y) (y - z)} + \frac{x}{(z - x) (x - y)} + \frac{z}{(y - z) (z - x)}$

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(ঘ)
$\frac{1}{x + 3 y} + \frac{1}{x - 3 y} - \frac{2 x}{x^{2} - 9 y^{2}}$

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(ঙ)
$\frac{1}{x - y} - \frac{2}{2 x + y} + \frac{1}{x + y} - \frac{2}{2 x - y}$

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(চ)
$\frac{1}{x - 2} - \frac{x - 2}{x^{2} + 2 x + 4} + \frac{6 x}{x^{3} + 8}$

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(ছ)
$\frac{1}{x - 1} - \frac{1}{x + 1} - \frac{2}{x^{2} = 1} + \frac{4}{x^{4} + 1}$

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(জ)
$\frac{x - y}{(y - z) (z - x)} + \frac{y - z}{(z - x) (x - y)} + \frac{z - x}{(x - y) (y - z)}$

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(ঝ)
$\frac{1}{a - b - c} + \frac{1}{a - b + c} + \frac{a}{a^{2} + b^{2} - c^{2} - 2 a b}$

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(ঞ)
$\frac{1}{a^{2} + b^{2} - c^{2} + 2 a b} + \frac{1}{b^{2} + c^{2} - a^{2} + 2 a b} + \frac{1}{c^{2} + a^{2} - b^{2} + 2 c a}$

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