Question:বিয়োগফল নির্ণয় কর: ক. `a/(x - 3) - a^2/(x^2 - 9)` খ. `1/(y(x - y)) - 1/(x(x + y))` গ. `(x + 1)/(1 + x + x^2) - (x - 1)/(1 - x + x^2)` ঘ. `(a^2 + 16b^2)/(a^2 - 16b^2) - (a - 4b)/(a + 4b)` ঙ. `1/(x - y) - (x^2 - xy + y^2)/(x^3 + y^3)`
Answer ক. `a/(x - 3) - a^2/(x^2 - 9)` `= a/(x - 3) - a^2/(x^2 - 3^2)` `= a/(x - 3) - a^2/((x + 3)(x - 3))` ` = (a(x + 3) - a^2)/((x - 3)(x + 3))` ` = (ax + 3a - a^2)/((x - 3)(x + 3))` `= (ax + 3a - a^2)/(x^2 - 9)` উত্তর: `= (ax + 3a - a^2)/(x^2 - 9)` খ. `1/(y(x - y)) - 1/(x(x + y))` `= (x(x + y) - y(x - y))/(xy(x - y)(x + y))` `= (x^2 + xy - xy + y^2)/(xy(x - y)(x + y))` `= (x^2 + y^2)/(xy(x - y)(x + y))` `= (x^2 + y^2)/(xy(x^2 - y^2)` উত্তর: `= (x^2 + y^2)/(xy(x^2 - y^2)` গ. `(x + 1)/(1 + x + x^2) - (x - 1)/(1 - x + x^2)` `= ((x + 1)(1 - x + x^2) - (x - 1)(1 + x + x^2))/((1 + x + x^2) (1 - x + x^2))` `= ((x - x^2 + x^3 + 1 - x + x^2) - (x + x^2 + x^3 - 1 - x - x^2))/((1 + x^2 + x) (1 + x^2 - x))` `= ((x^3 + 1) - (x^3 - 1))/((1 + x^2)^2 - x^2)` `= ((x^3 + 1) - (x^3 - 1))/(1 + 2x^2 + x^4 - x^2)` ` = (x^3 + 1 - x^3 + 1)/(x^4 + x^2 + 1)` `= 2/(x^4 + x^2 + 1)` উত্তর :` 2/(x^4 + x^2 + 1)` ঘ. `(a^2 + 16b^2)/(a^2 - 16b^2) - (a - 4b)/(a + 4b)` `= (a^2 + 16b^2)/(a^2 - 16b^2) - (a - 4b)/(a + 4b)` `= (a^2 + 16b^2)/((a + 4b) (a - 4b)) - (a - 4b)/(a + 4b)` `= (a^2 + 16b^2 - (a - 4b)^2)/((a + 4b) (a - 4b))` `= (a^2 + 16b^2 - (a^2 - 2.a.4b + 16b^2))/((a + 4b) (a - 4b))` `= (a^2 + 16b^2 - (a^2 - 8ab + 16b^2))/((a + 4b) (a - 4b))` `= (a^2 + 16b^2 - a^2 + 8ab - 16b^2)/(a^2 - (4b)^2` `= (8ab)/(a^2 - 16b^2)` উত্তর: `(8ab)/(a^2 - 16b^2)` ঙ. `1/(x - y) - (x^2 - xy + y^2)/(x^3 + y^3)` `= ((x^3 + y^3) - (x - y) (x^2 - xy + y^2))/((x - y) (x^3 + y^3))` `= (x^3 + y^3 - (x^3 - x^2y + xy^2 - x^2y + xy^2 - y^3))/((x - y)(x^3 + y^3))` `= (x^3 + y^3 - x^3 + x^2y - xy^2 + x^2y - xy^2 + y^3)/((x - y)(x^3 + y^3))` `= (2x^2y - 2xy^2 + 2y^3)/((x - y)(x^3 + y^3))` `= (2y(x^2 - xy + y^2))/((x - y)(x + y)(x^2 - xy + y^2))` `= (2y)/(x^2 - y^2)` উত্তর :`(2y)/(x^2 - y^2)`
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biyogphol nirony karo: ka. `a/(x - 3) - a^2/(x^2 - 9)` kh. `1/(y(x - y)) - 1/(x(x + y))` ga. `(x + 1)/(1 + x + x^2) - (x - 1)/(1 - x + x^2)` gh. `(a^2 + 16b^2)/(a^2 - 16b^2) - (a - 4b)/(a + 4b)` ঙ. `1/(x - y) - (x^2 - xy + y^2)/(x^3 + y^3)`