Linear Equations Containing Fractions

Topic Content:

To solve simple equations containing fractions, first eliminate the fractions by multiplying each term with the LCM of the denominators and then solve as usual. 

Example 6.3.1:

Solve the following equation 

a. \( \frac{15}{x} \scriptsize = 3 \)

b. \( \frac{x}{7} \scriptsize = 4 \)

c. \( \frac{3x \: + \: 5}{5} \scriptsize = 4 \)

d. \( \normalsize \frac{2}{3} \scriptsize x \: – \: \normalsize \frac{8}{5} \scriptsize = 5 \)

e. \( \normalsize \frac{3}{2x} \scriptsize \: + \: \normalsize \frac{1}{6x} \scriptsize = \normalsize \frac{2}{3} \)

f. \( \normalsize \frac{2x \: – \: 5}{4} \scriptsize \: – \: \normalsize \frac{6x}{2} \scriptsize = 0 \)

Solution 

a. \( \frac{15}{x} \scriptsize = 3 \)

We have only one denominator, multiply through by the denominator ( x )

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