Question

Consider the rational equation 1/R=(1/x)+(1/y).Find the value of R when x=2/5 and y=3/4.

Answer 1

Answer:

R =  $\frac{6}{23}$

Step-by-step explanation:

Given the rational equation as:

$\frac{1}{R}=\frac{1}{x}+\frac{1}{y}$

To find:

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

and, y = $\frac{\textup{3}}{\textup{4}}$

now,

substituting the given values of x and y in the given rational equation,

$\frac{1}{R}=\frac{1}{\frac{2}{5}}+\frac{1}{\frac{3}{4}}$

or

⇒ $\frac{1}{R}=\frac{5}{2}+\frac{4}{3}$

or

⇒ $\frac{1}{R}=\frac{5\times3+4\times2}{2\times3}$

or

⇒ $\frac{1}{R}=\frac{15+8}{6}$

or

⇒ $\frac{1}{R}=\frac{23}{6}$

now on rearranging, we get

⇒ R =  $\frac{6}{23}$