Question
Solve for $x: \frac{1}{x+4}-\frac{1}{x+7}=\frac{11}{30}, x \#-4,7$.
✓
Answer
$\frac{1}{x+4}-\frac{1}{x+7}=\frac{11}{30}$
$\frac{x+7-(x+4)}{(x+4)(x+7)}=\frac{11}{30}$
$\Rightarrow \frac{3}{x^2+7 x+4 x+28}=\frac{11}{30}$
$\Rightarrow 90=11 x^2+121 x+308$
$\Rightarrow 11 x^2+121 x+218=0$
$\Rightarrow D=b^2-4 a c$
$=(121)^2-(4 \times 11 \times 218)$
$=14641-9592$
$D=5049$
and $\sqrt{D}=71.05$
Now, $x=\frac{-b \pm \sqrt{D}}{2 a}$
$=\frac{-121 \pm 71.05}{22}$
$\Rightarrow x=-2.27$ or $x=-8.73.$
$\frac{x+7-(x+4)}{(x+4)(x+7)}=\frac{11}{30}$
$\Rightarrow \frac{3}{x^2+7 x+4 x+28}=\frac{11}{30}$
$\Rightarrow 90=11 x^2+121 x+308$
$\Rightarrow 11 x^2+121 x+218=0$
$\Rightarrow D=b^2-4 a c$
$=(121)^2-(4 \times 11 \times 218)$
$=14641-9592$
$D=5049$
and $\sqrt{D}=71.05$
Now, $x=\frac{-b \pm \sqrt{D}}{2 a}$
$=\frac{-121 \pm 71.05}{22}$
$\Rightarrow x=-2.27$ or $x=-8.73.$
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