5/x+3 take away 1/x-2 equals to 1. solve two possible answers for x

Question 1

Question 2

Answer:

$\qquad{:}\longrightarrow$
$\sf \frac {5}{x+3}-(1)/(x-2)=1$

$\qquad{:}\longrightarrow$
$\sf \frac {5 (x-2)-1 (x+3)}{(x+3)(x-2)}=1$

$\qquad{:}\longrightarrow$
$\sf \frac {5x-10-x }{x^2-6x-6} =1$

$\qquad{:}\longrightarrow$
$\sf 5x-x-10=x^2-6x-6$

$\qquad{:}\longrightarrow$
$\sf x^2-6x-6=4x-10$

$\qquad{:}\longrightarrow$
$\sf x^2-6x-4x-6+10=0$

$\qquad{:}\longrightarrow$
$\sf x^2-10x+4=0$

$\qquad{:}\longrightarrow$
$\sf x=\frac {-b\underline{+}\sqrt {b^2-4ac}}{2a}$

$\qquad{:}\longrightarrow$
$\sf x=\frac {10\underline{+}\sqrt {(-10)^2-4×1×4}}{2×1}$

$\qquad{:}\longrightarrow$
$\sf x=\frac {10\underline{+}√(100-16)}{2}$

$\qquad{:}\longrightarrow$
$\sf x=\frac {10\underline{+}\sqrt {84}}{2}$

$\qquad{:}\longrightarrow$
$\sf x=\frac {10+\sqrt {84}}{2}\quad or\quad x=\frac {10-√(84)}{2}$

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