SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]x^2=\frac{2x}{x+1}[/tex]
STEP 2: Simplify the equation for x
[tex]\begin{gathered} \mathrm{Multiply\:both\:sides\:by\:}x+1 \\ x^2\left(x+1\right)=\frac{2x}{x+1}\left(x+1\right) \\ \mathrm{Simplify} \\ x^2\left(x+1\right)=2x \end{gathered}[/tex]
STEP 3: Solve the resulting polynomial equation
[tex]\begin{gathered} \mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides} \\ x^2\left(x+1\right)-2x=2x-2x \\ x^2\left(x+1\right)-2x=0 \\ Factorise \\ x\left(x-1\right)\left(x+2\right)=0 \\ \mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0 \\ x=0\quad \mathrm{or}\quad \:x-1=0\quad \mathrm{or}\quad \:x+2=0 \\ \mathrm{The\:solutions\:are}: \\ x=0,\:x=1,\:x=-2 \end{gathered}[/tex]
Therefore,
[tex]x=0,x=1,x=-2[/tex]
Hence, the answers will be as seen below:
