Question:যোগ নির্ণয় কর: ৩.ক. `(a - b)/a + (a + b)/b` খ. `a/(bc) + b/(ca) + c/(ab)` গ. `(x - y)/x + (y - z)/y + (z - x)/z` ঘ. `(x + y)/(x - y) + (x - y)/(x + y)`
Answer ক. `(a - b)/a + (a + b)/b` `= (b(a - b) + a(a + b))/(ab)` `= (ab - b^2 + a^2 + ab)/(ab)` `= (a^2 + 2ab - b^2)/(ab)` উত্তর: `(a^2 + 2ab - b^2)/(ab)` খ. `a/(bc) + b/(ca) + c/(ab)` `= (a^2 + b^2 + c^2)/(abc)` উত্তর: `= (a^2 + b^2 + c^2)/(abc)` গ. `(x - y)/x + (y - z)/y + (z - x)/z` `= (yz(x - y) + zx(y - z) + xy(z - x))/(xyz)` `= (xyz - y^2z + xyz - z^2x + xyz - x^2y)/(xyz)` `= (3xyz - x^2y - y^2z - z^2x)/(xyz)` উত্তর: `= (3xyz - x^2y - y^2z - z^2x)/(xyz)` ঘ. `(x + y)/(x - y) + (x - y)/(x + y)` `= ((x + y)^2 + (x - y)^2)/((x - y)(x + y))` `= (x^2 + 2xy + y^2 + x^2 - 2xy + y^2)/((x + y)(x - y))` `= (2x^2 + 2y^2)/(x^2 - y^2)` `= (2(x^2 + y^2))/(x^2 - y^2)` উত্তর: `= (2(x^2 + y^2))/(x^2 - y^2)`
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jog nirony karo: ৩.k. `(a - b)/a + (a + b)/b` kh. `a/(bc) + b/(ca) + c/(ab)` ga. `(x - y)/x + (y - z)/y + (z - x)/z` gh. `(x + y)/(x - y) + (x - y)/(x + y)`