Answer:
R = [tex]\frac{6}{23}[/tex]
Step-by-step explanation:
Given the rational equation as:
[tex]\frac{1}{R}=\frac{1}{x}+\frac{1}{y}[/tex]
To find:
The value of R when x = [tex]\frac{\textup{2}}{\textup{5}}[/tex]
and, y = [tex]\frac{\textup{3}}{\textup{4}}[/tex]
now,
substituting the given values of x and y in the given rational equation,
[tex]\frac{1}{R}=\frac{1}{\frac{2}{5}}+\frac{1}{\frac{3}{4}}[/tex]
or
⇒ [tex]\frac{1}{R}=\frac{5}{2}+\frac{4}{3}[/tex]
or
⇒ [tex]\frac{1}{R}=\frac{5\times3+4\times2}{2\times3}[/tex]
or
⇒ [tex]\frac{1}{R}=\frac{15+8}{6}[/tex]
or
⇒ [tex]\frac{1}{R}=\frac{23}{6}[/tex]
now on rearranging, we get
⇒ R = [tex]\frac{6}{23}[/tex]
