Question
11:16 5G siyavula.com Siy \( 2 \sqrt{u} / 2 \) Choose a language (question is not yet translated) Algebraic expressions (Part 2): factorisation SIMPLIFYING ALGEBRAIC FRACTIONS Simplify the following: \[ \frac{t-2}{2 t-4} \] INSTRUCTION: Your answer must be a fully simplified fraction or an integer. Answer: \( \square \) Check answer 2 attempts remaining Help! How should I type my answer? 95
Ask by Zimmerman Lawson. in South Africa
Feb 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the fraction is \( \frac{1}{2} \).
Solution
We start with the expression:
(t – 2) / (2t – 4)
Notice that the denominator 2t – 4 can be factored by taking 2 as a common factor:
2t – 4 = 2(t – 2)
Now the expression becomes:
(t – 2) / [2(t – 2)]
Since (t – 2) appears in both the numerator and the denominator, we can cancel it (provided that t ≠ 2, since division by zero is undefined):
(t – 2) / [2(t – 2)] = 1/2
Thus, the simplified form of the algebraic fraction is 1/2.
The answer is: 1/2.
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Simplify this solution Extra Insights
To simplify the fraction \(\frac{t-2}{2t-4}\), start by factoring the denominator. Notice that \(2t-4\) can be factored as \(2(t-2)\). Now the fraction looks like this: \[ \frac{t-2}{2(t-2)} \] Since \(t-2\) appears in both the numerator and the denominator, you can cancel it out (as long as \(t \neq 2\), to avoid division by zero). This leaves you with: \[ \frac{1}{2} \] So the simplified answer is \(\frac{1}{2}\). A common mistake is forgetting to check for restrictions. It's crucial to note that if \(t=2\), the original expression becomes undefined due to division by zero. Always consider those restrictions when simplifying!
