Question

2/(x+3) + 6/(x+6)=1
quadratic equation, find x​

Answer 1

$\large \maltese \: \: \: \sf \underline{ \underline{Question \: : }}$

• Find the root or roots of the function 2/(x+3) + 6/(x+6)=1

$\large \maltese \: \: \: \sf \underline{ \underline{Solution\: : }}$

$\longrightarrow \sf \: \frac{2}{x + 3} + \frac{6}{x + 6} = 1$

$\longrightarrow \sf \: \frac{2( x + 6) + 6(x + 3)}{(x + 3)(x + 6)} = 1$

$\longrightarrow \sf \frac{2x + 12 + 6x + 18}{ {x}^{2} + 9x + 18 } = 1$

$\longrightarrow \sf 8x + 30 = {x}^{2} + 9x + 18$

$\longrightarrow \sf {x}^{2} + x - 12 = 0$

$\longrightarrow \sf {x}^{2} + 4x - 3x - 12 = 0$

$\longrightarrow \sf x \bigg(x + 4 \bigg) - 3 \bigg(x + 4 \bigg) = 0$

$\sf \longrightarrow \bigg(x - 3 \bigg) \bigg(x + 4 \bigg) = 0$

$\longrightarrow \: \: \underline{ \boxed{ \bf{x = 3 \: \: \: \: \: \: \& \: \: \: \: \: \: x = - 4}} \: \: }_{ \bigstar \star}$