Answer:
[tex]\frac{7}{6}[/tex]
Step-by-step explanation:
Given
a=1/5
b=1/2
c=3
d= -1/4
Required
[tex]\frac{1}{a} * \frac{1}{c} + \frac{1}{b} * d[/tex]
Substitute the values of a, b, c and d in the expression above
[tex]\frac{1}{\frac{1}{5}} * \frac{1}{3} + \frac{1}{\frac{1}{2}} * \frac{-1}{4}[/tex]
Simplify the above expression
[tex]1/{\frac{1}{5} * \frac{1}{3} + 1/{\frac{1}{2}} * \frac{-1}{4}[/tex]
[tex]1*{\frac{5}{1} * \frac{1}{3} + 1*{\frac{2}{1}} * \frac{-1}{4}[/tex]
[tex]5 * \frac{1}{3} + 2 * \frac{-1}{4}[/tex]
[tex]\frac{5}{3} + \frac{-2}{4}[/tex]
[tex]\frac{5}{3} - \frac{2}{4}[/tex]
Take LCM
[tex]\frac{20 - 6}{12}[/tex]
[tex]\frac{14}{12}[/tex]
Divide the numerator and denominator by 2
[tex]\frac{7}{6}[/tex]
Hence, [tex]\frac{1}{a} * \frac{1}{c} + \frac{1}{b} * d[/tex] = [tex]\frac{7}{6}[/tex]
