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

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]