Question

(1+1/x+1)(1-1/x-1)= 4/5​

Answer 1

Answer:

=(1+1*1-1)/x^2-1=4/5

=(2*0)/x^2-1=4/5

=0=4x^2-4

=4x^2=4

=x^2=1

=x=1

Answer 2

Step-by-step explanation:

• First write the given equation

$\qquad\qquad\sf:\longrightarrow (1+\dfrac {1}{x}+1)(1-\dfrac {1}{x}-1)=\dfrac {4}{5}$

• Simplify

$\qquad\qquad\sf:\longrightarrow (1+1+\dfrac {1}{x})(1-1-\dfrac {1}{x})=\dfrac {4}{5}$

$\qquad\qquad\sf:\longrightarrow (2+\dfrac {1}{x})(-\dfrac {1}{x})=\dfrac {4}{5}$

$\qquad\qquad\sf:\longrightarrow (\dfrac{2x+1}{x})(-\dfrac {1}{x})=\dfrac {4}{5}$

$\qquad\qquad\sf:\longrightarrow \dfrac {-1 (2x+1)}{x^2}=\dfrac {4}{5}$

$\qquad\qquad\sf:\longrightarrow \dfrac {-2x-1}{x^2}=\dfrac {4}{5}$

• use cross multiplication

$\qquad\qquad\sf:\longrightarrow 5 (-2x-1)=4x^2$

$\qquad\qquad\sf:\longrightarrow -20x+5=4x^2$

$\qquad\qquad\sf:\longrightarrow 4x^2+20x-5=0$

• a=4, b=20, c=-5

use quadratic formula

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

$\qquad\qquad\sf:\longrightarrow x=\dfrac {-20\underline{+}\sqrt {(20)^2-4×4×-5}}{2\times 4}$

$\qquad\qquad\sf:\longrightarrow x=\dfrac {-20\underline{+}\sqrt {400+80}}{8}$

$\qquad\qquad\sf:\longrightarrow x=\dfrac {-20\underline{+}\sqrt {480}}{8}$

$\qquad\qquad\sf:\longrightarrow x=\dfrac{-5\underline{+}\sqrt {480}}{2}$

$\qquad\qquad\bf:\longrightarrow x=\dfrac {-5}{2}+\dfrac {1}{2}\sqrt {30}\quad or\quad \dfrac {-5}{2}-\dfrac {1}{2}\sqrt {30}$