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Algebraic Fractions and Formulae

Secondary 2 practice

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Algebraic Fractions and Formulae practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Solve 2x+1−14x−5=0\frac{2}{x + 1} - \frac{14}{x - 5} = 0. Find the value of xx.
Show the worked solution
  • 2x+1−14x−5=0\frac{2}{x + 1} - \frac{14}{x - 5} = 0
  • 2(x−5)−14(x+1)=0multiply through by (x+1)(x−5)2(x - 5) - 14(x + 1) = 0 \quad \scriptsize\textit{multiply through by } (x + 1)(x - 5)
  • 2x−10−14x−14=02x - 10 - 14x - 14 = 0
  • −12x−24=0-12x - 24 = 0
  • −12x=24-12x = 24
  • x=−2x = -2

Answer: −2-2

Example 2

Express 3x+3−2x−1\frac{3}{x + 3} - \frac{2}{x - 1} as a single fraction.
Show the worked solution
  • 3x+3−2x−1\frac{3}{x + 3} - \frac{2}{x - 1}
  • =3(x−1)−2(x+3)(x+3)(x−1)LCM = (x+3)(x−1)= \frac{3(x - 1) - 2(x + 3)}{(x + 3)(x - 1)} \quad \scriptsize\textit{LCM = }(x + 3)(x - 1)
  • =3x−3−2x−6(x+3)(x−1)= \frac{3x - 3 - 2x - 6}{(x + 3)(x - 1)}
  • =x−9(x+3)(x−1)= \frac{x - 9}{(x + 3)(x - 1)}

Answer: (x−9)/((x+3)(x−1))(x-9)/((x+3)(x-1))

Example 3

Given that T=2+11xT = 2 + \frac{11}{x}, make xx the subject of the formula.
Show the worked solution
  • T=2+11xT = 2 + \frac{11}{x}
  • T−2=11xsubtract 2 from both sidesT - 2 = \frac{11}{x} \quad \scriptsize\textit{subtract } 2 \textit{ from both sides}
  • x(T−2)=11multiply both sides by xx(T - 2) = 11 \quad \scriptsize\textit{multiply both sides by } x
  • x=11T−2x = \frac{11}{T - 2}

Answer: 11/(T−2)11/(T-2)

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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