Chapter 5.3, Problem 52E

To determine

To calculate : the value of $x$

Answer to Problem 52E

The value of $x=\frac{5}{2}$

Explanation of Solution

Given information : The question is $\frac{1}{x}+\frac{3}{2x}=1$

Calculation : The denominator of the given fractions, factorize them:

  $\begin{array}{l}x=x\times 1\\ 2x=2\times x\end{array}$

Evaluate the least common multiple of the given numbers, use common factors only once

  $\begin{array}{l}LCD=2\times x\\ =2x\end{array}$

Now convert each fraction to an equivalent fraction such that its denominator is equal to the LCD

  $\begin{array}{l}=\frac{1\times 2}{x\times 2}+\frac{3\times 1}{2x\times 1}\\ =\frac{2}{2x}+\frac{3}{2x}\end{array}$

Now, the denominators are equal, so perform the indicated operations between the numerators

Therefore,

  $\begin{array}{l}=\frac{2+3}{2x}\\ =\frac{5}{2x}\end{array}$

Now equate this fraction with $1$ to solve for $x$

  $\frac{5}{2x}=1$

Multiply both sides of the equation with $x$

  $\begin{array}{l}\frac{5}{2x}\times x=1\times x\\ x=\frac{5}{2}\end{array}$