Latex demo

$$(क)\ \frac{a}{a-b} + \frac{b}{b-a}$$    $$\ \frac{a}{a-b} + \frac{b}{-(a-b)} $$ $$(ख)\ \frac{1}{b-c} + \frac{b+c}{b^2-c^2} $$ $$ (ग)\ \frac{1}{m-n} + \frac{1}{m+n} $$ $$ (घ)\ \frac{m+n}{m-n} + \frac{m-n}{m+n} $$ $$ (ङ)\ \frac{1}{m+n} + \frac{n}{m^2-n^2} $$ $$ (च)\ \frac{a^3+b^3}{a^2-ab+b^2} + \frac{a^3-b^3}{a^2+ab+b^2} $$ $$ (छ)\ \frac{4x^2 + 25y^2}{4x^2 - 25y^2} + \frac{2x - 5y}{2x + 5y} $$ $$ (ज)\ \frac{4x^2 + 25y^2}{4x^2 - 25y^2} + \frac{2x - 5y}{2x + 5y} $$ $$ (झ)\ \frac{4x^3 + a^4 - 8x^7}{x^4 + a^4 - x^8 - a^8} $$ $$ (ञ)\ \frac{x}{x-y} - \frac{x}{x+y} + \frac{2xy}{x^2+y^2} $$ $$ (ट)\ \frac{3}{a+3} + \frac{4}{a-3} + \frac{9a}{2(9-a^2)} $$ $$ (ठ)\ \frac{1}{x+2y} + \frac{1}{x-2y} + \frac{2x}{4y^2-x^2} $$ $$ (ड)\ \frac{a}{(a-b)(a-c)} + \frac{b}{(b-a)(b-c)} + \frac{c}{(c-b)(c-a)} $$ $$ (ढ)\ \frac{y-z}{x^2-(y-z)^2} + \frac{z-x}{y^2-(z-x)^2} + \frac{x-y}{z^2-(x-y)^2} $$ $$ (ण)\ \frac{x^2-(a-b)^2}{(x+b)^2-a^2} + \frac{a^2-(x-b)^2}{(x+a)^2-b^2} + \frac{b^2-(x-a)^2}{(a+b)^2-x^2} $$ $$ (त)\ \frac{p^2 + 7p + 12}{p^2 + 5p + 6} + \frac{2}{p^2 + 6p + 8} - \frac{3}{p^2 + 6p + 8} $$ $$ (थ)\ \frac{x + 3}{x^2 + 3x + 9} + \frac{x - 3}{x^2 - 3x + 9} + \frac{54}{4x^4 + 9x^2 + 81} $$ $$ (द)\ \frac{1}{x^2 - 5x + 6} + \frac{2}{4x - x^2 - 3} - \frac{3}{x^2 - 3x + 2} $$ $$ (ध)\ \frac{b + 2}{1 + b + b^2} - \frac{b - 2}{1 - b + b^2} + \frac{2b^2}{1 + b + b^4} $$ $$ (न)\ \frac{1}{1 - b + b^2} + \frac{1}{1 + b + b^2} + \frac{2b}{1 - b^2 + b^4} $$ $$ (प)\ \frac{a+c}{a^2 + ac + c^2} + \frac{a-c}{a^2 - ac + c^2} + \frac{2c^3}{a^4 + a^2c^2 + c^4} $$