Question

Please solve urgent please​

Answer 1

Answer:

$\frac{2}{x-3}+\frac{x}{x^2-9} = \frac{4}{x+3}\\ \\ \\</p><p>identity = a^2-b^2 = (a+b)(a-b) \\ \\ \\</p><p>x^2-9 = (x+3)(x-3) \\ \\ \\</p><p>lcm \: of\: (x-3) \:and\: (x^2-9) = x^2-9 \:as\: (x-3) \\ \\ \\ is \: a \: factor \: of \: it\\ \\ \\</p><p>\frac{2}{x-3} ×\frac{x+3}{x+3} = \frac{2(x+3)}{x^2-9} \\ \\ \\</p><p>= \frac{2x+6}{x^2-9} \\ \\ \\</p><p>\frac{2x+6}{x^2-9} +\frac{x}{x^2-9}\\ \\ \\</p><p>=\frac{2x+6+x}{x^2-9} \\ \\ \\</p><p>= \frac{3x+6}{x^2-9}\\ \\ \\</p><p>\frac{3x+6}{x^2-9} = \frac{4}{x+3}\\ \\ \\</p><p>by\: cross\: multiplication\\ \\ \\</p><p>4(x^2-9)= (3x+6)(x+3)\\ \\ \\</p><p>4x^2-36 = x(3x+6)+3(3x+6)\\ \\ \\</p><p>4x^2-36= 3x^2+6x+9x+18 \\ \\ \\</p><p>4x^2-36 = 3x^2+15x+18 \\ \\ \\</p><p>x^2-36= 15x+18\\ \\ \\</p><p>x^2-15x-36-18 = 0\\ \\ \\</p><p>x^2-15x-54= 0\\ \\ \\</p><p>by\: middle\: term\: splitting\\ \\ \\</p><p>x^2+18x-3x-54 = 0\\ \\ \\</p><p>x(x+18)-3(x+18)= 0\\ \\ \\</p><p>(x-3)(x+18) = 0\\ \\ \\</p><p>one\: of\: the\: term\: should\:become\:zero\\ \\ \\</p><p>x-3= 0\\ \\ \\</p><p>x= 3\\ \\ \\</p><p>x+18= 0\\ \\ \\</p><p>x= -18\\ \\ \\</p><p>therefore\:x=3,-18$