Question

Identify all values of that make the equation true.

Please explain them as step by step !!
Thank you!!

Answer 1

Part a

`(2x+1)/(x)=(1)/(x-2)\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=(2 \pm √(8))/(2)\\\\x=1 \pm √(2)`

Part C

`(x+3)/(1-x)=(x+1)/(x+2)\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=(-5 \pm √(-15))/(4)\\\\x=(-5 \pm i√(15))/(4)`