Answer :

Certainly! Let’s solve the problem step by step:

1. Define the fractions: We are given two fractions to sum: [tex]\(\frac{1}{30}\)[/tex] and [tex]\(\frac{1}{70}\)[/tex].

2. Sum the fractions: To sum the fractions, we need to find a common denominator. The denominators are 30 and 70. The least common multiple (LCM) of 30 and 70 is 210. Thus, rewrite each fraction with the common denominator:

[tex]\[ \frac{1}{30} = \frac{7}{210} \][/tex]

[tex]\[ \frac{1}{70} = \frac{3}{210} \][/tex]

Now, add the fractions:

[tex]\[ \frac{1}{30} + \frac{1}{70} = \frac{7}{210} + \frac{3}{210} = \frac{7 + 3}{210} = \frac{10}{210} = \frac{1}{21} \][/tex]

3. Reciprocal of the sum: We are given that the sum of the fractions equals the reciprocal of [tex]\(x\)[/tex]:

[tex]\[ \frac{1}{30} + \frac{1}{70} = \frac{1}{x} \][/tex]

From the calculation above, we know that:

[tex]\[ \frac{10}{210} = \frac{1}{21} \][/tex]

Therefore,

[tex]\[ \frac{1}{21} = \frac{1}{x} \][/tex]

4. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], take the reciprocal of both sides of the equation:

[tex]\[ x = 21 \][/tex]

Hence, the value of [tex]\(x\)[/tex] is 21.