Chapter 5.6, Problem 17WE

To determine

To simplify the given expression.

Answer to Problem 17WE

  $\frac{a^2+b^2+c^2}{abc}$

Explanation of Solution

Given:

Expression: $\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}$

Calculation:

Consider the given expression $\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}$ ,

Since the denominators of both the fractions are different, find the least common denominator for both the fractions.

Here, least common denominator is $abc$ , so

  $\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}$

  $=\frac{a\cdot a}{bc\cdot a}+\frac{b\cdot b}{ac\cdot b}+\frac{c\cdot c}{ab\cdot c}$

  $=\frac{a^2}{abc}+\frac{b^2}{abc}+\frac{c^2}{abc}$

Now, as the denominators of the two fractions are same, simply add the numerators and put the result on the same denominator.

  $\begin{array}{l}\Rightarrow \frac{a^2}{abc}+\frac{b^2}{abc}+\frac{c^2}{abc}\\ \Rightarrow \frac{a^2+b^2+c^2}{abc}\end{array}$

Conclusion:

Therefore, after simplification, the answer is $\frac{a^2+b^2+c^2}{abc}$ .