Chapter 5.9, Problem 7E

To determine

To solve the equation with fractional coefficients using given methods.

Explanation of Solution

Let us assume an equation with fraction as $\frac{2}{3}\mathrm{x}=\frac{12}{9}$ .

First method:

Multiply both sides by the LCD of the fractions.

Here we shall multiply both sides with 9, we get,

  $\begin{array}{l}\frac{2}{3}\mathrm{x}\left(9\right)=\frac{12}{9}\left(9\right)\\ 6\mathrm{x}=12\\ \mathrm{x}=2\end{array}$

Second method:

Use the above method for an equation having variable in the denominator.

Let the equation be $\frac{2}{3\mathrm{x}}=\frac{12}{9}$

Now we shall multiply with $9\mathrm{x}$ both sides we get,

  $\begin{array}{l}\frac{2}{3\mathrm{x}}\left(9\mathrm{x}\right)=\frac{12}{9}\left(9\mathrm{x}\right)\\ 6=12\mathrm{x}\\ \mathrm{x}=\frac{1}{2}\end{array}$

No extraneous roots have been introduced here. (But sometimes it is possible that extraneous roots may be introduced.)