While revising equations that involve fractions, a student is given the equation \(\frac{2}{x} + \frac{1}{3} = 1\), where \(x\) is not zero. Solve the equat...
Question 1 Report
While revising equations that involve fractions, a student is given the equation \(\frac{2}{x} + \frac{1}{3} = 1\), where \(x\) is not zero. Solve the equation to find the value of \(x\), showing full working at every stage. (4)
Answer Details
This question solves an equation containing two different algebraic fractions by clearing both denominators at once with a common multiple.
The two denominators are \(x\) and \(3\), so multiplying every term by their lowest common multiple, \(3x\), clears both fractions simultaneously:
\[3x \times \dfrac{2}{x} + 3x \times \dfrac{1}{3} = 3x \times 1\] \[6 + x = 3x\][1 mark]
Collecting the \(x\) terms on one side:
\[6 = 3x - x\][1 mark]
\[6 = 2x\][1 mark]
\[x = 3\][1 mark]
Checking in the original equation: \(\dfrac{2}{3} + \dfrac{1}{3} = 1\), which is correct. Multiplying every single term, including the \(1\) on the right-hand side, by \(3x\) is what allows both fractions to disappear in one step.
Download The App On Google Playstore
Everything you need to excel in your exams
