Question

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

Answer 1

Answer:

Solution:-

• First write the given equation

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

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

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

• use cross multiplication method

$\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$

• use quadratic formula

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

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

$\qquad{:}\longrightarrow$$\sf x=\dfrac {10\underline{+}\sqrt{100-16}}{2}$

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

$\qquad{:}\longrightarrow$$\sf x=\dfrac {10+\sqrt {84}}{2}\quad or\quad x=\dfrac {10-\sqrt{84}}{2}$