Question

Find the roots of the equation
$\frac{1}{x + 4} - \frac{1}{x - 7 } = \frac{11}{30}$
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Answer 1

$\dfrac{1}{x+4}-\dfrac{1}{x-7}=\dfrac{11}{30}\quad(x\not =-4 \wedge x\not =7)\\\\30(x-7)-30(x+4)=11(x+4)(x-7)\\30x-210-30x-120=11(x^2-7x+4x-28)\\-330=11(x^2-3x-28)\\11x^2-33x-308=-330\\11x^2-33x+22=0\\x^2-3x+2=0\\x^2-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-2)(x-1)=0\\x=2 \vee x=1$