Calculation:
Simplify the given equation by multiplying \(\displaystyle{\left({2.12}+{x}\right)}\) on both side of the equation as,
\(\displaystyle{\frac{{{1.73}{x}}}{{{2.12}+{x}}}}\cdot{\left({2.12}+{x}\right)}={1.51}\cdot{\left({2.12}+{x}\right)}\)

\(\displaystyle{1.73}{x}={3.2012}+{1.51}{x}\) Now, substract 1.51x on both sides of the above equation as, \(\displaystyle{1.73}{x}-{1.51}{x}={3.2012}+{1.51}{x}-{1.51}{x}\)

\(\displaystyle{0.22}{x}={3.2012}\) Now divide by 0.22 on both sides of the above equation as, \(\displaystyle{\frac{{{0.22}{x}}}{{{0.22}}}}={\frac{{{3.2012}}}{{{0.22}}}}\)

\(\displaystyle{x}={\frac{{{3.2012}}}{{{0.22}}}}\) Simplify the expression to two decimal places by use of calculator to obtain the value of x. \(\displaystyle{x}={\frac{{{3.2012}}}{{{0.22}}}}\)

\(\displaystyle{x}={14.550909}\)

\(\displaystyle{x}\approx{14.55}\) Therefore, the two decimal approximated solution of the given equation is \(\displaystyle{x}={14.55}\) Answer: The solution of the equation \(\displaystyle{\frac{{{1.73}{x}}}{{{2.12}+{x}}}}={1.51}\) for value of x rounded off to two decimals is 14.55.

\(\displaystyle{1.73}{x}={3.2012}+{1.51}{x}\) Now, substract 1.51x on both sides of the above equation as, \(\displaystyle{1.73}{x}-{1.51}{x}={3.2012}+{1.51}{x}-{1.51}{x}\)

\(\displaystyle{0.22}{x}={3.2012}\) Now divide by 0.22 on both sides of the above equation as, \(\displaystyle{\frac{{{0.22}{x}}}{{{0.22}}}}={\frac{{{3.2012}}}{{{0.22}}}}\)

\(\displaystyle{x}={\frac{{{3.2012}}}{{{0.22}}}}\) Simplify the expression to two decimal places by use of calculator to obtain the value of x. \(\displaystyle{x}={\frac{{{3.2012}}}{{{0.22}}}}\)

\(\displaystyle{x}={14.550909}\)

\(\displaystyle{x}\approx{14.55}\) Therefore, the two decimal approximated solution of the given equation is \(\displaystyle{x}={14.55}\) Answer: The solution of the equation \(\displaystyle{\frac{{{1.73}{x}}}{{{2.12}+{x}}}}={1.51}\) for value of x rounded off to two decimals is 14.55.