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Topic Content:
- Equations with Unknown Variables in the Denominator
Worked Example 9.2.1:
Solve the following:
i. \( \frac{12}{x} \; - \; \frac{2}{3x} = \frac{1}{6} \)
ii. \( \frac{4}{5x} = \frac{1}{35} \: - \: \frac{3}{7} \)
iii. \( \frac{2}{5x} \: - \: \frac{3}{2x} = \scriptsize 1 \frac{4}{7} \)
iv. \( \frac{2}{5} = \frac{1}{2y} \; - \; \frac{3}{4y} \)
v. \( \frac{5}{8} = \frac{10}{x}\)
vi. \( \frac{1}{x} = \frac{2}{7}\)
i. \( \frac{12}{x} \; - \; \frac{2}{3x} = \frac{1}{6} \)
Find the L.C.M
\( \frac{3(12) \; - \; 1(2)}{3x} = \frac{1}{6} \)
\( \frac{36 \; - \; 2}{3x} = \frac{1}{6} \)
\( \frac{34}{3x} = \frac{1}{6} \)
Cross multiply
\( \scriptsize 3x = 34 \; \times \; 6 \)
\( \scriptsize 3x = 204 \)
Divide both sides by 3
\( \frac{ 3x}{3} = \frac{204}{3} \)
\( \scriptsize x = \normalsize \frac{204}{3} \)
\( \scriptsize x = 68\)
ii. \( \frac{4}{5x} = \frac{1}{35} \: - \: \frac{3}{7} \)
Find the L.C.M of the right side
\( \frac{4}{5x} = \frac{1 \: - \: 15}{35} \)
\( \frac{4}{5x} = \frac{-14}{35} \)
Cross multiply
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